Imaginary Numbers - YourTeacher.com - Algebra 2 Help

[waynemv]

Sqrt(25) = 5 and not -5. That's because the square root function is defined as selecting the positive value. But that rule fails for sqrt(-25), as neither 5i nor -5i is positive.

It is usually understood that sqrt(-25) is an improper and ill-defined notation, since it has two solutions and no rule for picking which. The i symbol was introduced for the very purpose of eliminating the need to use the square root notation for negative numbers so that this very ambiguity could be avoided.

[MetapodMaster]

the stare at the end...it looks into your soul

[trainedtiger]

I think she is pretty, commence hating.

[bandet888]

In high school I was taught that the imaginary number is represented by the letter i (for imaginary of course). But when I went to college I was taught that the imaginary number was represented by the letter j not i. Supposetly the letter i was getting confused with amps in electronice (I studied electronics) So they decided to use the next letter in the alphabet which is j.

[waynemv]

@bandet888 Some people may try to tell you that i*j=k. Then they'll tell you j*i=-k. Seriously, the one has a negative sign and the other doesn't? Could mathematics be any more messed up than that?* Anyway, see the Wikipedia page titled "Quaternion" for more examples of their noncommutative insanity!

*The answer is yes, see octernions.

[waynemv]

@bandet888

P.S. the imaginary number j used in electronics is actually the negative of the imaginary number i used in algebra. So if anywhere you see a j you replace it with -i, the math will still work out just the same. :-)

[mogeroithe]

Nerdy women are hot!!!

[mogeroithe]

Ok... Question for the math nerds... The question asks for the square root of -25. Why would the answer not be -5? Why go through this complex process to get 5i?

[dudecoolname]

@mogeroithe There is no such thing as the square root of a negative. They can't exist. If you think about it, square root means two numbers that multiply together to get the original number. Does -5 time -5 equal 25? No....And there's your answer. To numbers (of the same sign) always end up as a positive number.

[mogeroithe]

@dudecoolname Yeah, I know all that. They also tell you that you can't multiply or divide a repeating decimal, but it gets done all the time. There may be a few rules that get slightly bent in the process, but it gets done just the same. With that being said, I can look at the problem above and instantly get an answer, without jumping through the hoops. My question, though poorly stated above is, what is the difference between -5 and 5i? Negative 5 is an imaginary number the same as 5i.

[dudecoolname]

@mogeroithe Negative 5 is not an imaginary number. It is a real negative number, negative numbers can and do exist. Imaginary numbers do not exist. There are no two numbers (with the same sign) that can multiply together to get -25, or any negative number.

-5 and 5i are two totally different numbers....for example 5i x 5i = -25...But -5 x -5 = 25. A better question would be "why do we even use imaginary numbers"...now that I have no fucking clue

[mogeroithe]

@dudecoolname This is where "book learnin" and the real world lose their nexxus. You cannot conceivably, except in the realm of magic and miracles, take an imaginary anything of any value and create something real out of it. Only God Himself can do that. I respect your education and I appreciate the time you have taken with me on this subject. I am not stupid by any means when it comes to math, but I disagree with a lot of what is being taught under the guise of "advanced math."

[mogeroithe]

@mogeroithe When you slow down long enough to consider what is being said by way of explanation, it violates the laws of common sense.

For instance, if you can swallow the idea that two negatives make a positive (which also applies in Grammar), then what you end up with in this instance is that -5 and 5 are one and the same. Because when you square them both, you end up at the same place. There is a dead rat in the wall somewhere. We need to find it.

[waynemv]

@mogeroithe In mathematics, the words "negative", "positive", "real", and "imaginary" are technical terms and mean only what they are defined to mean in the context, nothing more. The terms have nothing to do with whether such numbers exist in reality. How can any number be said to really exist when numbers are abstractions? Anyway, the kind of existence imaginary numbers have is no different from the kind of existence the real numbers have. If one is actual the other is too, and vice versa.

[waynemv]

@mogeroithe Complex numbers are necessary in order to have a complete system of algebra. Complex numbers had to be introduced because equations that were written using only real numbers would sometimes turn out to have solutions that are not real numbers.

Also historically, when mathematicians tried to solve some third degree polynomials, it was discovered that although the solutions were real numbers, the equations could only be solved by using complex numbers during the intermediate steps!

[dudecoolname]

-25*

[alligatorcloud]

oh dear lord her voice



[alinusD]

why when she finishes the video her nose gets 10 times bigger?

[IPMountainDew]

so basically you just normally do it without the negative and place an 'i' next to it. I thought this was 4unit stuff.

[imairborne123]

Holy shit, I. Doing this next year O.o

[estesoyojajaja]

if i use imaginary numbers with the problem 2+2, is it possible to me to get another answer but 4?

[hnddbbdac]

Math...gotta hate it.

[SuperWHAAAAAAAT]

COULD YOU DO A HARDE PROBLEM LIKE SQUARE -16

WOULD THE ANSWER BE 8ISQAURE 2

[IPMountainDew]

@SuperWHAAAAAAAT the answer to -16 would be 4i

[IPMountainDew]

@SuperWHAAAAAAAT answer to -16 would be 4i (i = square root -1)

[Smael64]

slaps head at realization of how simple it is

[DeadInDecadence1]

apple mann!!

[azxc49]

can anybody tell me what you do when you have a (-) outside the radical?

[AMAZINGPHILstalker]

Why must she talk like a robot?

[mrhindo]

@AMAZINGPHILstalker

cuz she IS A ROBOT!!!

[genedirks]

OMG What happened to the other guy? It's a sad world when online math teachers get replaced all willy-nilly!

[SENYAP19]

Yes.. This is a good video.. Since negative square root of five can't be solve, by inputting imaginary numbers helps a lot :)

[rsw2009]

jeez, i already have a hard enough time with numbers let alone IMAGINARY ones

[NeuterSkooter]

Why learn something that isn't real!

[MyOverflow]

@NeuterSkooter Imaginary numbers are used extensively in electrical engineering.

[AEVautomatic]

@MyOverflow nopers ive been an electrical engineer for more thta 50 years and worked on complex projects like the LHC. I was cheif electrical engineer for LHC and ive neve once in my life used head of anyone useing seen anyone use or talk about imaginary numbers.

[MyOverflow]

@AEVautomatic I guess it really must depend on what you're doing in electrical engineering, because I know some electrical engineers that have told me that they use imaginary and complex numbers on a daily basis in their jobs, so I was going on what they've told me.

[RectumPilum]

42:0= SHIIIIIIIITTTTTTTTTTTTTT!!!!

[AndrewLeonardi]

I love you.

[kingsaravia1]

Does anyone wonder why we have to learn about imaginary numbers? In other words, numbers that don't exist?

[BuddhistmeansWisdom]

@kingsaravia1 Visualizing Imaginary Numbers: There is an unrevealed major breakthrough! No Bluff! Imaginary Numbers are no more confusing! How would you value such indepth understandings? Nothing is free to be shared... Make a genuine offer! Welcome to the new generation of Mathematics! Able and interest, will contribute with sponsorship. Spread the word... Thank you. Reply to: grlm_bandara@yahoo.co.uk (Mr. Lakshan Bandara)

[kingsaravia1]

@BuddhistmeansWisdom

???

[drewsufff]

@kingsaravia1 No imaginary numbers are important not just because they actually do exist, but also they are used in a lot of mathematical fields. For example engineers work with imaginary numbers in a lot of their calculations, because for some reason (I don' know yet), their calculations yield imaginary numbers as well, so knowledge of imaginary numbers is required in order to distinguish the real from the imaginary values.

[kingsaravia1]

@drewsufff

That barley makes any sense.

[seeker9969]

Ok where did you get the 5 from in this video.

[Lasershot117]

@seeker9969 Sqrt(25)=5

[1loby]

What's up with math these days?

[Miley101Cyrus101HM]

It's so hard to understand but ao easy at the sametime

[valensmann]

Actually the video is wrong, unless there are multiple definitions of i, but only i^2 is -1. Not i.

[aprilmornin]

@valensmann No, as you said: i^2=-1 which means that i=sqrt of -1, so the video is correct.

[scout6686]

this chick is more nerd than I can take.

[mrhindo]

@scout6686

yea... lol she will remain a virgin

[estesoyojajaja]

@scout6686 I got a joke for you: Pi and i where argue, and i told Pi Be rational and Pi told i Get real. Hahaha

[scout6686]

@estesoyojajaja haha nice

[estesoyojajaja]

@scout6686 i forgot, thumbs up if you did like it.

[TRANNSVESTITEPONY]

@scout6686 imagine how tight she'd be.

[BONIFASI007]

or + or - 5

[mario32]

would you be able to use 1 in any equation that involves the square root of any number say the square root of 72?

[theimaginarynumber]

@mario32 Do you mean i?

[ikillyou121]

yes, but you would get a wierd value between 8 and 9 i.

[Balticmania]

-5i is also a solution. Why was this omitted?

[ParadigmaticShift]

because -5i is not a solution.

[Balticmania]

I've checked Google and Yahoo and both state that both i and -i are solutions to the square root of -1, so it follows that 5i and -5i should be the square roots of -25. If you type (-5i)*(-5i) in Googol, the calculator comes up, displaying the result of -25.

[theimaginarynumber]

Correct.

[DevoutSkeptic]

@Balticmania That's because the square root of -1 is +/- i, just as the square root of 1 is +/- 1.

[arghydoodles]

@Balticmania That's the same Google that can only translate Germanic languages.

[VoguishArts]

@Balticmania The internet is a great source for learning right? You learn and actually hold more knowledge, rather than in a school being taught by some moron trying to make a living with ease.

[Puertoricanlips]

thanks

[RealAthenius]

This is very helpful but personally I found imaginary numbers to be easy.

[docnelson2000]

Exactly what is the point of all this and what use is it to our daily lives?

[Visoball5550]

engineers use it for electrical and structural purposes. einstine used it for alot of his theorems

[drrrerr]

what the fuck..

_/-25 is impossible

you cant square root minuses

stop making stuff up

[logical123]

It's impossible in the Real Number set, but not in the complex or Imaginary sets. It's basic algebra, really.

[dudeEGGS01366]

this kid is fuckin stupid

[HandyBendyGandhi]

lol - nobody's making anything up -logical123 is absolutely correct. Look up 'imaginary numbers' in wikipedia if you don't believe it.

[ilovetoskateboarding]

but rmember dibshits write stuff in wikipidia to

[HandyBendyGandhi]

Ok then look up 'imaginary numbers' in ANY book on advanced mathematics.

[ilovetoskateboarding]

its possibal. but not logically. thats why its called imaginary

[IshikawaKohai]

the imaginary number was created to make an answer to square roots with negative numbers in them

if there were no imaginary numbers the answer to the square root of -25 would be an impossible answer, but with i, the answer can be defined as 5i

[shootnmove]

good response

[dsmith951]

is i only relevant if its the square root of -1?

[shootnmove]

no, theres 4 ways I is use

i - i squared - i cubed - and i to the 4th power...

and they just repeat after that

[MyNameIsAshleyB]

This is why I hate math and why I suck at it. It just seems so retarded to have imaginary numbers...I need concrete stuff. My brain doesn't understand this type of math...I mean I get this one but we all know it can get a lot more complicated than that.

[cornetstadium]

omg i love this. its like dumbed down math. why cant my teacher teach like this?!??!?! its sad when you have to go to youtube to learn math..

[Doggieman1111]

she has excellent chalkboard handwriting

[drrrerr]

what the fuck..

_/-25 is impossible

you cant square root minuses

what the fuck

[koenarens]

mate u can with i

[drrrerr]

what the fuck..

_/-25 is impossible

you cant square root minuses

what the fuck

[simplyivan16]

ummm . . . first of all, chill! This is just math. Second of all, yes you can . . . with help of 'i'

[drrrerr]

what the fuck..

_/-25 is impossible

you cant square root minuses

what the fuck

[shootnmove]

what you have to do is realize that i = square root of -1... then like she says its root -1 (or i) times root 25.... thus 5i is the answer

[drrrerr]

you're crazy

[spike0804]

but hes perfectly right

[loveashley213]

hey this is easy, i thought it was way harder. thanks lots!

[robjbrooker]

She should conclude that the square roots of -25 are 5i and -5i, not just 5i

[luvCher4ever]

no the square root of 25 is 5, not 5 and 5.

[robjbrooker]

The square roots of -25 are 5i and -5i.

If you doubt it, try squaring -5i .

[luvCher4ever]

oh sorry I misunderstood you. :)

[micsibulopianist]

wow... nice... it's very helpful...

[NateFab4]

Really Helpful Video but she talks like a nerd. lol

[PureExile]

Which mathematical theorem are you using to deduce that √(-25)=√(-1)√(25)? It is certainly true that √(ab)=√a√b for all non-negative real numbers a,b but it is not true that √(xy)=√x√y for all real numbers x,y. For example,

1 = √1 = √[(-1)(-1)] ≠ √(-1)√(-1) = i.i = -1.

[mjimbooyah]

The logic is incorrect. square root of somehting has both positive and negative answers and thus your statement should be i. (-i) = +1.

[PureExile]

The symbol "≠" means "is not equal to". You seem to be suggesting that 1≠1.

[mjimbooyah]

hi

what i am suggesting is that the equation is true for all real numbers provided you consider there are 2 solution for any square roots. one minus and the other positive. So 1 = square root of 1= Square root of minus one multiplied by square root of minus one = positive i mulitiplied by negative i= positive one. (of course youcan also consider square root Positive i x positive i ornegative i x negative i which give wrong answers.

[PureExile]

I'm not sure what you are on about. Please see my videos "1+1=0: The Proof!" and "1+1=0: The Flaw!" here on YouTube. It is certainly correct that √(-25)=5i but I left the comment in the hope that someone from yourteachermathhelp would tell us WHY √(xy)=√x√y if and only if x≥0 or y≥0.

[xjuhox]

Hmmm...

My swedish language teacher once gave me grade 'i' from one exam when the scale was 4-10!!

So did I really get imaginary unit or what was it?

[SshikitO]

COOL VIDEO TY

[eldominicanboy]

cool, now i get it