 Hello everyone and welcome to Tutor Terrific. Today I have the TI84 plus CE calculator to do a tutorial for you. This will be like a beginner tutorial to show you the basic ropes and get your head around this thing and how to use it for basic stuff. This calculator is very well sought out for these days. If you're not willing to switch to the TI Inspire, this is kind of the most recent high-end high-tech version of the TI84 lineup and so I think it deserves a tutorial like this. So before we get started pressing buttons I want to show you some basic hardware stuff. This calculator is a rechargeable battery and so on the side you have your port. Now you're going to get with the calculator a mini USB cable and an adapter. So don't lose those because mini USBs is kind of outdated and you're going to need to charge this every now and then. Once it's charging and you've plugged it in properly this orange light will shine to let you know it's charging. Rechargeable batteries are in here and using rechargeable batteries of course allows this to be a lot thinner than the older versions of the TI84 Plus for example. Note also that on the back side this might come in handy to you. A reset button. A reset button will allow you to set all the settings as if it was brand new out of the package and kind of get you out of a sticky situation in case there's something wrong with the calculator. Okay now the cover also it comes with a cover mine is used so ignore the scratches but that allows you to protect the thing. You can turn it upside down and slide it into the slots for better protection and keep that case with you by turning it over and sliding it in. If you're familiar with any scientific calculators you're well aware of that for all of them. Okay let's get to some button pressing. We're going to press the on button to turn this thing on down here and the first thing I want you to notice is that this is backlit so I can turn all the lights off and you can still see the screen just fine. Don't worry I will be working like that because it's quite hard to see the screen without the backlight and this is an LED display. Now there's another older TI-84 that is LED display as well but just note that it has backlighting in case you have a power issue or a lighting issue so that is a nice feature but it definitely uses a lot more juice and so a rechargeable battery is a nice feature for these. Notice also if I put this closer the battery level indicator currently it's all the way up with that nice green bar as you deplete the battery that green bar goes down becomes red and eventually it depletes all together and it's just a hollow red battery icon and you need to get that thing charged quick. Make sure it's nice and charged before you go on a test or if you have to go away and study and you forget the cable. Don't get caught in this situation where you're about to take a test and this thing dies on you. You can't just put new batteries in it because it's not that type of battery so just word to the wise don't lose your cable and charge it frequently. Okay so to turn it on press the on button like I did and to turn it off we activate the second button here so the second and alpha if you're unfamiliar are buttons that allow you to access more features without having to add extra buttons on the user interface here. If you want to activate any of the blue words or features you press the second button and you press the button underneath that feature for example if I wanted a square root I would press the second button and the x squared but I want to turn the calculator off so I'm pressing second and also I wanted to point out did you notice how the screen went dim but not completely off that's a feature I think about after about 30 seconds of idle time it's going to go to that dim setting to save battery and then after a brief period more of not touching it it will turn completely off it'll go to sleep we say just to save that battery for you so nice features to help you prolong the life of this thing now I've got second I've got that selected you know it is selected because there's an arrow in the middle of your blinking cursor so if I press any button it will activate the blue text above it in this case off so that's how you turn your calculator completely off if we turn it back on I want you to notice something else all these words at the top so all these words at the top here are some of your settings important settings in your calculator that I was currently set at I'm going to show you next how to get to those settings okay and that's called the mode menu a very important menu think of it like your settings menu for your calculator if we open that up we see all these different settings not the best display but it's kind of a classic display for all the ti 80x series so each row is a setting for example the top one which isn't blinking right now I'm going to move this blinking cursor down with the down arrow as you can see I've got multiple settings here the top setting is an important one it's how you want to view your expressions do you want to view them in the math print mode which was made famous by another scientific calculator in ti's lineup the ti 34 multi view or the 30 sx2 multi view it allows you to see equations and expressions like you would in your textbook or you can switch that to classic mode which is more of the classic texas instruments interface which doesn't really have some of the nice features of making exponents really small or new raters and denominator type fractions smaller so like one can be over the other uh if you don't like that for example you want to switch a setting note that the setting that's currently selected is the one that is in black it's highlighted in black with a black background so if you want to switch to something else for example I want to switch to classic mode come up here and move the cursor over to the right so the classic is selected and press enter now note that classic itself is uh highlighted instead of math print and I want math print because I think it's far superior so I'm going to select that there's lots of other settings here such as the type of angle unit we're using the type of graphing we're doing what type of coordinates we're doing and many other settings that we might or might not get into all right to get out of the mode menu you could do two things you could press clear or you can press a more important button that we need to learn called quit if I press second then mode notice over here since it can't really show me the arrow here so obscure what I'm highlighting it puts the second here so that I can know that the second has been selected so if I press mode it's going to activate quit which is going to get me back to my main uh operation input menu uh window okay so that's the mode menu you're going to be in there quite a bit adjusting modes depending on what class you're in let's do some simple arithmetic checking order of operations works let's try five plus nine times three should it do the multiplication first yes and we should get 32 if it does the addition first we would expect to get 42 so let's see what happens perfect as you would expect order of operations is done and loaded in here correctly okay we can also do division on this calculator eight divided by five for example it's going to show it like this there's ways to get that to be changed and we'll look at that later but you would expect eight slash five if the division symbol is used to mean divide by five and that is exactly what you get you get 1.6 which is eight divided by five so arithmetic operations are actuated with these buttons over here plus minus multiply and divide okay now one thing that's really nice about these features these calculators is that you can recall your previous entries for a long time now if uh before i show you that i just want you to show how you can clear your palette here because you don't want to see anything just press the clear button now if you want to see your previous history of calculations that you've done you just press the up arrow if you press it once you see the previous answer if you press it twice you see the previous operation that got you that answer and if you keep going up with the up arrow you go one line up in the past to your previous calculations let's say you wanted to uh do one of those calculations again but you didn't want to type it all out for example six minus i times six plus i i'll talk about i later if it's blue and highlighted if you press enter it will bring it down and make it your new expression that you want to evaluate and if you press enter it will evaluate it again okay that's a great tool now another great tool for recalling old calculations you've done is uh second entry now as you can see my previous entry was this six plus i times six minus i if i press second and then the entry button see how it's entry blue above the enter it's going to recall that previous entry and allow you to do it again and if i press second entry once it recalls the previous transaction if i press second entry again it will recall the next one in the list up if i do it again it's going to recall my previous one which as you saw was eight divided by five and you can keep pressing second entry over and over again to get a more previous uh calculation that you've done and press enter to evaluate it pressing clear we'll clear this out so we don't see all that anymore another useful feature is the an s using the previous answer let's get our five plus nine times three back or 32 now let's say i wanted to do some stuff to 32 maybe subtract six times nine notice how i started writing minus six times nine and it already put this a and s there that a and s represents my previous answer that's 32 loaded into the calculator so we'd expect 32 minus six 26 times nine oh my gosh a big number close to 260 oh no it's going to do six times nine for silly me i forgot order of operations there it's going to do that 54 and it's going to do 32 minus 54 silly me so that's the calculator checking me on my bad order of operations all right if we clear that i want to show you how you to get a and s without having to type some operation first you can write currently the previous answer was negative 22 you can recall that a different way you can press second and then the negative sign that negative sign is different than the minus sign okay if you press second negative sign you see a and s is up there what it is just done is load that negative 22 that we previously got as an answer and now i can do something to it such as add five get negative 17 a useful feature but they don't only recall the very last answer you got nothing previous to that okay now what we're going to do next is we're going to look at some other operations that are a little bit more complicated than just your basic add subtract multiplier divide for example let's look at things that are here like for example i already mentioned the square root if i wanted to take a square root of something i would write the second and then see this x square button if i press that i'll get the square root and then i'll type in what i want inside there and you notice i type a number i'm still inside the radical symbol and i can add more things as requested by myself or if i wanted to get outside the radical i could press the arrow when i'm at the end see how it's got an arrow blinking it says if you click it one more time you're going to get out of the radical and now i can do stuff outside the radical if i so desire okay so that's the square root the square button is that same button but you don't press second first so let's say we've got uh let's see what's a nice square uh perfect square 49 so if i've got 49 here and i want to square all i have to do is press x squared and then we have our x squared 24 01 now what if you wanted to uh do a different square uh different square root so like a root to a different power a different degree of root or a different degree of exponent rather than two there's a couple ways to do that if you want uh the um uh a number to a higher power other than two you can press the number you want to raise to the exponent and then come up here to what's called the carrot button if you press that carrot button you can add any exponent up in this space notice how i've moved to the superscript of the three i've moved to that position and so i can put you know anything i want in there obviously i wouldn't want to calculate that it's going to be crazy but for example three to the sixth notice that when i press the arrow once after putting my exponent in it gives me this right arrow saying if you do it one more time you are going to get out of the exponent position into the main level position maybe you want to add something but if you want to go back and change the exponent you can do that by pressing the back arrow the left arrow until you get back up there into the superscript position and let's say you wanted to change that exponent to be not six but six minus five now at any point no matter where you are your cursor your blinking cursor is in your expression you can press enter and it will evaluate it just fine we'd expect that to be nine three to the six minus five power three to the one power is three plus six is nine i didn't have to move the cursor to the end of the expression i'm going to bring this back down like i taught you before i didn't have to have the cursor here in order to evaluate it it's the same answer so just you less clicks less clicking of different things saves you time especially if you're on a timed test where you need to get through it to make sure you get the the best grade you can you want to save clicks for sure okay so that's uh raising to any power we can also uh do uh if we're going to do things to any power we should also look at scientific notation things times tend to a power okay so let's do that now the button to get uh 10 to the x is a shortcut here you see how it's uh the second of logarithm l o g so generally speaking you can press second log and then it shows 10 to an exponent notice how i didn't have to type in the 10 for example 10 to the eighth press enter get 100 million now if you use this you're most likely using it for scientific notation so i want to show you there's two ways to do this you can use this button or the double e button here so let's say you want to write something in scientific notation and see what it looks like in standard notation 9.2 or 9.36 times and then press second log to get that 10 to the and then for example 10 to the nine it's going to output the standard form of that number all the place holding zeros which scientific notation likes to avoid so you can see what that actually equals in standard notation now you don't actually need to type the multiplication to do this 9.36 and then skipping the times you can go straight to the 10 to that with the second log and type that same exponent nine and look press enter you get the same result so you actually can skip that which is kind of nice it's a time saver now there is another way to do scientific notation and it's a shortcut so a couple less buttons to press and that's by actuating this double e here so let me show you why this is useful 9.36 instead of going to second log we're going to go second comma okay now we're going to type the same exponent now what we've done here is we've written 9.36 times 10 to the nine that e represents times 10 to the okay so far we haven't saved much of any steps but this is useful because if you type in something massive you're trying to get the calculator to do something massive and it doesn't have enough digits to do that in standard notation it's going to give you the answer in scientific notation for example this massive product here notice the answer is 1.475 80667 to e 17 you have to understand that and interpret that to be for example if i round this 1.48 times 10 to the 17 so the calculator uses this notation when it spits out big answers so you need to be aware of that and it also does it for really small answers okay it'll just have a negative number there if the number is too small for it to have enough digits to write it in standard notation so that's why i like using double e when i was in physics in college i just used that because i liked the notation better it was less clunky you just have to get used to it so those are two ways to do scientific notation if we can do things raising to the power of 10 we should be able to do raising things to the power of e okay and there's a button for that it's second l n which stands for natural log e to the five for example is done that simply press enter and you have e raised to the power of five so that's a way to deal with e now in addition to that there's also an e over here you see on the division symbol so i can press second divide and i just get e by itself if i don't want to raise it to a power but i'd like to like multiply it by three i can do that with that button you can't do with the other one because it's expecting an exponent you'd have to put one in there if you just meant to deal with e by itself okay let's also talk about the inverse operations to these exponential functions the logarithm and the natural logarithm so the logarithm is this base button here 10 underneath the 10 to the x you press that log it shows you log with a parentheses let's put what we want to take the log of let's do something nice that will give us a nice answer 10 000 so as you know logarithms spit out the exponent required to turn 10 into this number you plugged in that should be a four and we get a four like we expect so note that the log button defaults to base 10 logarithms the common logarithms if you want to change the base there's ways to do that with a special menu which a little too advanced for what we're going to do today or you can use the change of base formula which i can go over in another video leave that note in the comments for me if you want to see that and another important logarithm is the natural logarithm so down here we see our ln so i type that it's gonna tell me what exponent i have to raise e2 to turn it into what i plug in 2 is a very important number what power do i have to raise e2 to turn it into the number 2 0.693 a very important result used all the time you see all the time in math and physics and etc so there's your natural logarithm your logarithm and now what i want to show you is a little bit of memory features on this calculator what i'd like to show you now is how to store a value as a variable let's say you've got this number 10 and if you're in physics you know how important that number is or 9.8 for you who have a little bit more accurate number the acceleration due to gravity so let's say we want to store that so we can use that all the time let's say we want to store that as g which is how you see it in physics how do you do that well you press you put the number in that you want and then you press the st o which is a store button notice that when i press that button i get this little arrow here which says what would you like to store that as well in the alpha menu i'm going to press alpha and notice the cursor has a blinking a in it that lets you know you're on the alpha menu now it's going to actuate any of the green buttons above the buttons you see so we're looking for g which is above the tangent button so if i press g now g shows up there this is going to store 10 as g if you press enter you get the result 10 but the idea is every time i type g it's going to understand that as 10 well let's see if it does alpha g i type g and i press enter boom it spits out 10 saying g is equal to 10 i can also do things with g multiplied by five and then subtract six what should i get 44 five times 10 is 50 minus six is 44 so it's using g in calculations let's say you forget what you assigned to a variable how can you recall that information well there's a button for that press second store and you see rcl there rcl shows up at the bottom so it doesn't get in the way of what you're doing press alpha and g it's going to tell you what g means 10 and notice how it puts it up there for you so you can now use it to do things you might want to do with it so that's an interesting memory feature that you might find useful if you use the value over and over and over again throughout a class or a homework assignment or even a test now how do i uh work with the memory i've got all this memory here all these things i've done let's say i've i'm running out of room my calculator is telling me memory is getting full and these calculators do have finite memory how do you deal with that and get rid of that uh or clear your memory to give you room on your calculator to do more stuff well there's this memory menu down here if you press second plus you get to this menu okay the about just tells you about your calculator but two tells you uh your memory stats if i press enter there look what it tells me it tells me how much ram is free okay i think that's measured in bytes so you got about 152 megabytes or 153 megabytes free of ram now come tell me the comments if i'm wrong about that so uh there's lots of different types of memory and programs as well it's going to be a big one if you're downloading games and you can clear all of these or any of these at once let me show you how to clear them all because that's probably something you're going to do more than anything else to get out of this menu we can press second quit or clear go back to the memory by parking pressing second plus and now look down here at three and four three is going to clear entries all the calculations you did on the main one new and number four is going to clear all lists which we haven't got into because lists i think it's going to be its own video if you're doing stats no me know in the comments if you want to see that video so if you press three or enter when three is highlighted we get this now there's nothing more we need to add we haven't done any clearing of memory yet but if i press enter i've cleared my entire memory of all the entries into the calculator okay so what happens when i scroll up to look at my history i see one entry and that is that i cleared everything so next what i'd like to show you is the math button this is a button with a lot of sub menus that you're going to use quite a bit some basic stuff you need to do in this calculator the math button is right here and if you click it you get this now these capital letters are sub menus with things underneath them and you're going to use potentially quite a bit of these things throughout all of your math classes or your mathy science classes let's start with the first two buttons in the math sub menu fraction and decimal these allow you to convert what you have to the opposite type for example a decimal to a fraction number one and a fraction to a decimal number two so if i type uh go back to the main menu and i type a fraction that i have here as a decimal 2.58 okay and i want to see that decimal as a fraction i'm going to type the math button and then either type the number one or press enter when one is highlighted like this and then it populates that on the main entry screen and this is going to convert 2.58 to a fraction and there we have and it's going to reduce it as much as possible okay 129 over 50 now if i want to see that 129 over 50 as a decimal instead just for simplicity i'm going to highlight and enter it so now i have a fraction i want to see that as a decimal i'm going to press the math button go down to number two press enter or just press the number two now we have 129 over 50 number arrow des which means i'm going to turn this into a decimal and there you have the result written as a decimal really useful it's right there makes it easy for you to convert between the types i know other calculators that are scientific have a little double arrow button here which allows you more quickly to do that um yeah they just didn't have room on this calculator there's really not a spot for it to get this nice design they wanted so that is one really important feature of the math button if i clear this i want to show you something else in here and the shortcuts for cubes and cube roots huge you use those quite often almost as much as squares and square roots so they're down there in the number three and number four positions on this menu so let's say i wanted to cube something three cubed for example all i have to do is type three and then math three and there it is i like how they made it math three that makes it easy to remember that that's how you do that shortcut of course you could do the carrot and the three button with no extra steps but you might forget about that carrot button the math three i have a feeling you're going to remember more what if you want to cube root something you're going to press math four and now you have the cube root the radical works the same way as the square root that i showed you earlier you can type some stuff in here and if you want to get out of it you have to press the left arrow on the sorry the right arrow and the left arrow will get you back underneath it so i can now add something in there since i'm now back in there and uh whether i'm in or not i can press the enter sign and get the same result so that is the cube root feature really nice and handy because those are used all the time next let's look at the uh next thing in the math section i wanted to go over which is higher order roots so higher order roots number five there as i said before i can do higher degree roots like fourth root fifth root etc but what i have to do first is i have to input the degree i want to do for example let's try the fifth root of 32 so what we're going to do is we're going to uh type that degree first and then press math five and notice how it puts it right in the degree position which is really kind of cool and then you can type what you want inside there the radicand and press enter and you get what you'd expect which is a two so that's how you can do higher order roots another important thing that you use all the time absolute value so we go to the math menu and now we're going to scroll over with the right arrow key to the number menu and we'll see abs first it's not anti lock brake system that's absolute value in short now if you press one on it or you press enter sorry press enter if you're on one or just one no matter where you are you get this in the entry screen and this is meant to be absolute value of and now we can put what's in there i'll try negative 14 by the way if i haven't mentioned this uh negative symbol is here the minus sign is here and you can't mix those up where you'll get a syntax error and press enter whether i'm inside the absolute value symbols those vertical lines or not it will uh work and it will enter the proper expression and evaluate it as 14 which it should so that is a good feature whether you're inside your function or not you can press enter and it will evaluate as if you're not intervening at all okay now uh another thing i want to go over are some of the combinatorics of functions for those of you doing permutations and combinations you'll need to know how to do uh npr ncr and just simple factorials so let's say i wanted to find eight factorial and if you're not familiar what a factorial is you're just taking a number and multiplying it by every positive integer less than it all the way down to one so a factorial would be eight times seven times six times five times four times three times two times one so that's a lot to write out especially with larger numbers and so there's got to be a shortcut for that well if you type the number you want to do that with you go to math and you scroll over to probability and you press four or highlight four and press enter you see an exclamation mark that's the symbol for factorial in math and you just press enter and there we go 40 320 that's eight factorial so let's say you do factorials and back to this menu uh npr and ncr so let's say you want to do 12 p3 i'm not going to teach you you know what this means it's kind of assumed you already know what we're doing we're taking 12 objects and finding the number of ways to permutate them taken three at a time so if we go down here type enter at two you'll see you get a spot to put something a p and then a spot to put something else so we're going to take the total amount n of our list put that there and then hit the right key once and now we'll get to the r position to put how many things we're taking at a time and uh notice how i'm still down there at the bottom if i want to do something else in this expression and i want to like add something to this whole 12p3 i need to make sure i'm not still down there i have to click right because if i don't look what's happening i'm still i'm changing my r value i can clearly get out of hand and make r bigger than n which is not allowed so go back here delete that if you've accidentally do that and press the right key now you can see the cursor uh is full size so if i wanted to do anything additional like add six now it would be appropriate to do that but i don't want to do that for this i just want to press enter and get my 1320 if i want to do ncr instead go back to the math menu go to probability menu ncr which is three click that now i'm finding the ways to take three objects uh from 12 uh without worrying about order so we're going to get a smaller number here for 12 choose 3 220 so those are where those functions are for doing any combinatorics now one other thing i want to show you are some of the features of the fraction submenu in here go back to math and if you go all the way over to fraction notice how i did a click the arrow four times to get over there there's a better way this is a revolving menu that you can go through in a circular sequence so i could go backwards one left from math and get to fraction as well just you know finding ways to reduce the number of clicks is always good so the first two allow me to create fractions of these types the first one number one that's numerator over denominator a traditional fraction and uh improper fractions are also allowed and then u n over d is a mixed number so if i type a one it's going to show me this which is nice i can do what i did before calculating eight over five now i know it's a little hard to see uh i've got i'm in the numerator right now and um i am typing things in the numerator if i want to get to the denominator to type a five down there i have to press the down arrow just once i type the five and i'm still in the denominator if i want to get out notice what's showing in my cursor a right arrow click the right arrow once and now we have a fraction what this is going to do if i press enter is just retrieve the same fraction it's not going to do what i did before when i typed eight divided by five straight into the entries and gives me a decimal so just realize that but don't worry you can select this press enter and then go to the math menu and press two now this tried and true fraction is going to turn into a decimal let's just keep that in mind now if i want to write out a mixed number straight away go to the fraction submenu press two now you can see i've got the whole number in front one and three over five this allows me to uh write a mixed number it's going to put that by default into improper fraction form okay just keep that in mind some other things in this submenu is this the f to d let's see what this does let's see if you could imagine what this is going to do okay so first i'm going to go populate the entry with something let's do this okay one and three fifths and let's type that button three here look what it does it changes it from a fraction to a decimal now what i'd like to do is see if it will switch the form back from decimal to fraction let's click the same button fraction submenu three and look what it does so whatever form it's in it will change it to the other form if it's a decimal it'll make it a fraction and over d type so if the numerator is larger it will be improper or if you have a fraction it will turn it into whether it's improper or mixed number it will turn it into a decimal so that's a useful feature if you just want to get from decibel to fraction and vice versa there's more in here and that is the final button i haven't got over number four which turns a numerator denominator type fraction into a mixed number so if i have eight fifths here plug that here type that last one four boom so this is all of the features in the math button window you're going to be using that a lot now what i want to show you and it's very important in equation-based operating systems that there's some system for this is to edit your expressions before you enter them maybe making a correction of some kind so you don't have to re-enter everything let's say you had like i've done before five plus nine times three and you're like no i want to fix that and you accidentally press enter oh no i have to write the whole thing again right wrong go back up select your expression okay if let's say you wanted to add a negative in front of the three remember that the negative sign is here the minus signed traction is here don't mix them up or you'll get a syntax error what i want to do is put a negative right in front of the three there are two ways to do that first thing you can do is go to the three make sure it's the cursor is on top of it and you can type negative three so now instead of rewriting the entire expression i have now just changed a part of it okay i can go back even farther if i go back farther what you have to realize is what i'm doing is overwriting so it's going to overwrite what's currently there let's say i want this to be negative nine not nine well what is going to do is put a negative if i have the nine highlighted where the nine was now there's no nine there so i'm gonna have to type the rest of this expression that i want in order to get the entire negative sets that i want negative nine and negative three there's a better way to do this doesn't require you to rewrite half or all of the expression and that is the insert feature so let's put our entry in again let's say i wanted that to be negative nine and wanted this to be negative three scroll over to the nine don't start writing a negative instead press second delete look at what's happening now it's not the normal cursor anymore it's an underline cursor instead it blinks to an underline underscore what you will do now is type something and it will put it in front of whatever's blinking so and see how it added a negative in front of the nine without erasing the nine this is not overwriting however it will revert back to the overwriting style if you do anything left or right with the the cursor notice now i have a regular blinking cursor if i press a negative now it's going to replace the times with a negative so if i want to insert a negative in front of the three i will put the cursor on top of the three press second delete three will now be blinking with the underscore press minus sorry press the negative sign and then you can press enter of course those negatives cancel out and we get 32 again if you have an extra digit instead let's say you did five plus nine times negative negative three oops i didn't mean for that extra negative to be there scroll over to the digit or symbol you want to delete and press regular dl and it goes away now this next feature you may be doing this a lot or you may not has to do with complex numbers fully complex numbers that have imaginary parts such as dealing with i which is the square root of minus one if we want to call i into our entry it's down here it's the decimal points second for example if i press second and the decimal point i get a little i there that is not like all the green letters in the alpha mode in the alpha menu it is i the square root of minus one if i multiply it by two we would hope to see two i that doesn't prove what i'm saying but it does make it in the format of a complex number that we like to see which is what it defaults to a plus b i now i can do any of these operations that we've seen before arithmetic arithmetic adding subtracting multiplying dividing with i just as we would and we learn in our algebra classes so let's add two complex numbers together six plus three i and i'm using that traditional format of real plus imaginary part a plus b i and i'm going to add to that nine minus six i we would expect it to add like parts real parts together and imaginary parts together and look it does that 15 minus three i okay we can also do multiplication or division which really shows that it knows what i is let's do a division problem where it becomes very evident i'm going to go to the math menu and i'm going to set up a nice fraction so you can see what you might see in your math books if you're asked to divide a complex number by another so let's do a five minus i in the numerator press the down arrow to get to the denominator and then i see there's a glare here so let me move that over slightly sorry about that three focus five minus i over three plus three i notice how i always press a second decimal to get the i and whether i'm in the denominator or not i can press enter and it's going to evaluate that as it should two thirds minus i you would get this the same way by doing it multiplication of the complex conjugate of the denominator as you may have learned in your class for algebra notice how it gives the answer in the a plus bi format b in this case just happens to be one so very useful very very beneficial you can also do exponents with i let me clear this i can take i here and raise it to any power i wish and if you're familiar with imaginary numbers you know that i the exponents of i are cyclic in multiples of four so we would expect for example i to the 26 since that's two after a multiple of four to be the same as i squared so be negative one and there it is so this calculator has a full set of features to make use of all operations that you need with i the imaginary number there is one window associated with complex numbers in the math menu it's a submenu of math called complex c m p l x now there's some really cool features here we're going to go through two of them together the real and imagine okay if i click real and i type a complex number into it six plus 17 i for example and press enter by the way you may have thought do you always have to close these parentheses no it won't give me an error for syntax when i don't it just assumes it's closed it gives me six back when i press enter and that's just the real part of this fully complex number and i shouldn't say fully complex all numbers are complex but this has a real and imaginary part next let's go back to math and let's go to the complex submenu again and click image for imaginary okay let's type that same imaginary number in this time i'll close the parentheses i'm ocd and i like things to be closed because sometimes we need to add more on to our entry including division so it's good to practice putting those parentheses closed but in this case it doesn't matter if you do or don't what this is going to give me these the imaginary part of this complex number 17 it spits out the b of your a plus bi notice it doesn't put the i with it so the next thing i'm going to show you guys is graphing this is a graphing calculator after all so where are the graphing buttons and how do we do some basic graphing on here well they're up here at the top okay to enter a function to graph we have to go over to the y equals button and press that first when you do that you might see some preloaded fractions that were there from the last time this was used if you don't want those and you could press clear when each line is highlighted in some way you can go down and up to get to each and every uh y equals position now why they're more than one well you can graph up to 10 things at the same time in addition to plots which again has to do with stats and lists and comment below if you want one of those videos for me to go over that i'm not going to go over that in this video okay let's say we just want to graph a simple linear function x plus three y equals x plus three well the y is already there the independent variable is already there but how do i get the x the dependent sorry the dependent variable y is already there for all these functions how do i get the independent variable x it's this button right here and that will be an x if you're in the function mode on the calculator not the parametric polar or whatever that other one is i don't even know um so if we're in the function mode second quit to get out of this y equals to go back to where we were when you type that button you get an x okay let's say we want to do x plus three type that right away if you want to quickly figure out what that looks like we press graph it loads it on the screen which is kind of nice from left to right as if you were graphing it yourself and notice how it grasses a blue thick line those settings can be changed if we go back here and we scroll to the right two buttons press enter now we can adjust the color and the line thickness or style so let's turn that into a light blue line and we can change the line style to be thick dots for example press the down arrow once to press to okay these changes notice how it looks different over there so now if we press graph again it's graphing thick dots and a blue line the reason it looks thicker is because these thick dots are really close together but that is my line that i just graphed now i can graph more than this on the same graphing window we can go down here and let's say we want to graph good old parabola x squared so type x and then the squared button to square my previous entry x squared press graph again what a normal thickness line we got that beautiful x square parabola showing up and you may have noticed this but the there's some distortion in that y versus the x axis notice how the x axis tick marks are more separated than the y axis tick marks this is so you can fit 10 above and 10 below the origin in the y direction and 10 to the right and 10 to the left in the x direction get the same number of tick marks they're just not able to be as separated because this is not a square well there are ways to change that if you prefer to see a different number of tick marks or a different part of the cartesian coordinate plane and that is done through two different windows first i'm going to show you the zoom window which lets you adjust a zoom for what you're seeing on the plane that's graphed and one feature of course is to zoom in if we press two or enter when two is highlighted we go back to the main window nothing's happened yet but if i want to zoom i press enter again notice how i don't know if you could see it let me get this closer notice how the there's a dot blinking in the middle i can adjust where that is if i so desire that's just where the zoom is centered kind of like if you're doing transformations the center of your dilation so i can adjust that if i so desire normally you just want that in the middle of your screen so at the origin if we press enter it's going to zoom about the origin and so we're looking much closer you can notice that there's only like two tick marks in either direction showing up now let's say you wanted to zoom out you press zoom again since we're zoomed in if we press three it's going to zoom out back to what it was originally if i press enter there we go now let's say you didn't want this distortion if you go to a window here is how you can adjust the distortion but let me explain what you're looking at first you are given the left most x tick mark the right most x tick mark so the far left to the far right as far as the value of each tick mark is concerned on the screen how they increment how much you add to the previous tick mark to get the next one from left to right and then the lowest tick mark on the y axis the highest tick mark on the y axis and how they increment so this is basically your standard setup negative 10 to 10 with an incrementation of one each and that's fine and that gives you that distortion but it gives you the same number of tick marks so if you want to remove that distortion what i found works well is negative six y min to positive six y max notice how when i started to type at the beginning it just a rate it just populated or raised the previous entry for that and put a six in place even though there were two digits before so if i click graph now it's going to keep those settings notice how the tick marks are about as spaced out on the y axis now as the x axis so it's a useful tool for you if you do not like the distortion you want to see things more standard one more zoom feature i want to go over for you is standard zoom this is going to reset all the settings for the window it's going to erase all the settings we did put everything back to negative 10 10 and 1 as far as the min max and the uh incrementation on the y axis so just press 6 as you can see now we're back to what we were before if we click window everything's been reset so that's an easy way to do a reset there's also a trig zoom if we want to zoom so that we could see standard tick marks for trigonometric uh graphing which would be your uh half fractions of pi much better than 1 2 3 etc that's how you get that if i press that now it's not going to do much that means anything to you but we'll get to that when we're doing some trig function work a little bit later in this video all right now trace is an important button to know it's right here if we go trace what we're doing is we're currently going to follow one of these functions and see what its values are notice how there's an x value and a y value for the current position that's highlighted if i scroll to the right it's going to follow the function and tell me what value that pixel is on the screen so for a lot of the time these won't really follow the nice values you might have hoped for when you're on a grid on your paper but it gives you the idea of where you are on the graph if i want to switch between graphs so if i want to be on the parabola instead i'm going to click the down arrow you see all the numbers are now red my second function is up there and now i'm following the parabola around and i can go left and right thankfully it does give you that value the origin really nicely and you can follow that guy up and see the values at certain spots maybe see how x and y vary together but there's a much more useful feature than just randomly going to different parts of the function and that is second trace which gives you the calc menu if i type second trace i get here i can calculate a value anywhere on the graph if i so wish for example if i'm on my first function which it will default see y1 if i would like to calculate a value for something i can pick a particular spot for which i want to be to the left and right of and then i can adjust uh my boundaries so i have selected a left bound you see the arrow shows that's my left bound i'm going to be picking a value to the left of that and i'm going to scroll up here just an arbitrary distance and it's asking me what my right bound is i'm going to press enter and so it's got a cursor and a little line there and what it's doing now if i press enter again is it's going to tell me this is my first error message for you guys that there's no sign change calculations are not detecting a sign change to give an estimated result for the allowed number of iterations so what it wanted me to do for this value window is it wanted me to calculate basically where the sign changed for the dependent variable now there's a much easier feature we're going to erase that whole part where i talked about the calculate value we're going to skip that i'm going to show them something more useful so if we click second calc and we go down to this zero menu we've got a really really useful tool to find the roots or the zeros of a function now let's do a zero for the blue function okay y equals x plus three what you want to do to find a zero find where it crosses the x-axis first notice how it says left bound what we're going to do is we're going to move our cursor until we're to the left of that spot where it crosses the x-axis look at me holding it down and it's sliding on by so once you know you're to the left of that spot where it crosses the x-axis that you're trying to calculate press enter notice how it gives you an arrow and a line you're going to find a zero to the left of this line now let's go when it says right bound we're going to move up beyond the zero we want to calculate to the right of it and press enter now it gives me a right bounded arrow which means i'm finding a zero in between these two arrows all i have to do now when it says guess which i i don't like it's actually trying to calculate it i just don't understand the software that says guess but anyway press enter again it finds that zero perfectly and it gives you the coordinates of the zero x equals sorry negative three and y equals zero so you got a coordinate point of negative three zero so that's a very useful tool for sure if you're doing some advanced algebra or even calculus you want to know how to calculate those types of things but maybe you want to calculate something else for example a minimum or a maximum see down there a menu option three for a minimum now on the linear function this doesn't mean anything but on that parabola you could see a minimum value at the origin so we're going to press down to get to the parabola function y2 equals x squared and we're going to put our cursor on the left side of that minimum somewhere to the left of it and press enter and for the right bound we're going to move past the minimum somewhere beyond it to the right of it and press enter and then as you might have guessed we're going to press enter again it's going to find the smallest value between these two bounds and there it is notice what you get you don't get zero zero like you'd expect to get these weird scientific notation numbers but notice what they are they're extremely small 1.56 times 10 to the negative six it's like one a millionth and then you've got 2.436 times 10 to the negative 12 okay those are basically zero and it's a little glitch in the system that they just haven't figured out after all these years even the tiad3 plus did this you just assume when it does that that that means zero okay if any of you have more insight on that that'd be awesome to know you could do lots more in this menu the calculation menu including find a derivative so slope at a certain point do an integral if you're doing calculus and you could find where two functions intersect and I do want to show you that because it's a little different the way you show the buttons you press so let's press five so what we want to do is select our two curves if you have more than two curves or two graphs you need to select which two you want to find the intersection of so we only have two so I need to press enter and then the second curve well I only have one more to pick from so I press enter and then I press enter a third time and it's going to tell me the intersection and it's picking one picking the one that I have to be that have to be closer to the two positions where I selected enter before and it gives me the exact spot where they intersect if I wanted to find the other intersection up here press second calc and then intersect we need to move our cursor on the function close to that spot at least closer than the other intersection so that it will know that I want to find that intersection instead it will move you straight vertically not horizontally separated but straight up and down to the other function press enter press enter again notice how this time it found the closer intersection and the coordinates are listed below of course if you picked black as your color on the white equals menu some of this stuff would show up a little bit better than it does the numbers would be a different color but that is some of the basics of graphing on this calculator last but certainly not least trig functions basic things you need to know how to use on your graphing calculator where are the trig functions I'll get to that but first I want to go to the mode menu and show you the two types of angle units you have down four levels is radian and degree so currently it's in radian mode which will calculate if you're doing any trig functions it will assume all the inputs to them are radian measures of angles if you wish to switch that to degree you'd have to slide over here and press enter when degree is highlighted and blinking now anything you plug into a trig function it will assume it's a degree angle so we'll keep it on that for now second quick to get out it will save all your setting changes let's do sine of 30 degrees so where are the trig functions they're right here these buttons right here and their inverses not their reciprocals their inverses are the seconds second buttons okay so let's do sine of 30 degrees I do not need to find the degree symbol anywhere it assumes that this is degrees I don't I'll have to close the parentheses I will just for good measure and I get what I'd expect one half okay if I wanted to do a reciprocal trig function the cosecant the secant or the tangent what I have to do is I have to do the reciprocal of the trig function literally in the calculator there are several ways to do that I'm going to show you the non-confusing way as far as notation for example let's do the cosecant of 30 which we'd expect to be two what we're going to do is we're going to write one over sine of 30 and that will evaluate the cosecant of 30 there is no button here for csc there is no button doing inverse sine is not cosecant so don't assume that those are the same thing they're exactly not okay if I want to find for example an inverse trig function and actually know what I'm doing and I want to find the angle for which the sine value is one half I would type second sine okay and that second sine now gives me inverse sine so I'm going to type the value of the sine for that angle and it's going to give me the angle as the output of course in degrees because I am in degree mode if I switch back to radian mode in the mode window and press second quit and if I do inverse sine again of 0.5 it's going to give me the radian equivalent of 30 degrees pi over six as a decimal an irrational decimal but we can verify that that's equal to pi over six by clicking the pi button here second carrot divide by six what do you know pi over six so it's good to know where that pi is now you know now that we're in radian mode I can deal with pi and use these beautiful pies instead of decimals let's say we want the cosine of pi over two cosine second carrot divide by two close a parentheses if you want press enter we should get zero as we expect so these trick fungers can take their domains are infinite all real numbers they should be able to take negatives and positives of course they do tangent of negative pi over four okay notice how I put a minus sign in here I want to show you what happens error syntax okay you cannot mix negatives and minus signs if you want to fix something if you get this window you go back to it by pressing two and it will show you that entry that had a mistake it will show you the character will be highlighted blinking that caused a problem you can adjust it by overriding it with what you want which is a negative sign and you get negative one so that's it's the inverse and regular uh trick functions okay and their reciprocals as well if you want to graph something that is a trick function you can do that okay we're just going to adjust the zoom before we graph it let's see you just want to graph a simple sign of x plus two when you're graphing it's best oops we didn't want to do that so we're going to override that and put plus two outside because I want to raise the whole graph by two when you're graphing it's good practice to be in radian mode because the zoom trick feature assumes you're in radian mode and creates good pi over two fractions uh well pi over two multiples as the tick marks which is what you want in radian mode so we want to make sure in radian mode before we graph or it's going to be really stretched out and we're not going to know what's going on so we've got that here we're in radian mode go to zoom and press seven or go down and highlight zoom trig okay you can see your beautiful graph there and the tick marks are pi over two pi three pi over two two pi five pi over two etc the other way the uh y-axis tick marks are integers one two three and you can see how this sign graph because I moved it up two is centered at two on the y-axis it actually goes through it too so that my friends is graphing with trig functions and all the trig function features that you might need when you're getting started so I hope you guys have enjoyed this video I know it was quite long leave in the comments if you want further you know more specific videos on a certain feature happy to do that for you I want to serve you guys because you guys watching this hitting the like button subscribing serves me as well all right guys thanks for watching this is falconator signing out