Complex Numbers - Multiplying and Dividing

[iloveschultze]

CLEP College Mathematics tomorrow--fingers crossed!

[patrickJMT]

@iloveschultze god luck!

[MegaAbulik]

very good

[1337kakash1]

I learned more in this 7 min. video than I did in my 50 min. Alg. 2 class...

[gelucadri]

Thanks a lot!

[soccergirl2277]

My math teacher has the worst monotone so i can never pay attention so thank you for saving my test for tomorrow

[Brosnake9000]

Thank you so much bro!

[hassan4lifee]

how old are you!? are you like some old teacher? or just a student? cause if you're just a student, DAMN! you're good! i mean, every time my algebra 2 teacher teaches something in math (because she's such a horrible teacher) i come straight to you. props man! :)

[DarkB1ueKnight]

u know when i think of a lifesaver i usually think of a guy by the beach sitting on a high chair with a high visibility jacket on, after university that perception has changed to patrickJMT

[patrickJMT]

@DarkB1ueKnight ha : )

[DrPsymotion]

You dont flip the sign in the middle but the sign in front of i (3i-6 is not 3i+6 but -3i+6)

[blahblahblahman]

So easy lol thanks. I don't know why I only learn when I self-study and/or watch videos. I've never learned anything from a teacher in class. Everyone learns differently I guess.

[DrPsymotion]

@blahblahblahman teachers at school dont give a damn if they students learn something (most of them at least) and they are ussually bored which boredom transfers to the kids

[ANNAiSMR]

If i pass my final tomorrow it will be because of u !

[patrickJMT]

@ANNAiSMR good luck :)

[thiagohy1]

thanks man

[MrGreenerCat]

Sometimes I narrate myself doing math to try and be like you.

[patrickJMT]

@MrGreenerCat hahah

[andreww84nig]

thanks so much dude, you helped me pass my test lol

[Nfentis01]

i daydreamed during class today and this saved my butt for tmmrs quiz on all of this

[patrickJMT]

@SARSVLOG dont be a stupid troll, if possible.

[waleedsrahmatullah]

In the end...how did you get -5i+6 from 5i over -1 - 6 over -1 ?

[azamdeen]

I m fan of u Patrick...!!! Lov u alot...!!



[patrickJMT]

@azamdeen  : )

[coolerthanmeize]

how do u find upper and lower bound of this-->x^4+8x^3+24x^2+32x+16(P­olynomial and rational functions) it was on my quiz and people were talking about using the quadratic formula but i didn't how i could have found out the upper and lower bound if i had done the synthetic division and the quadratic thing...please help!! :D btw ur videos really helpful, i started watching them like a month ago and they really help hehe :)

[1Onsokumaru1]

PatrickJMT: saving failing grades one step at a time

Cannot thank you enough, dude

[patrickJMT]

@1Onsokumaru1 glad i could help you out : )

[HJAnglez]

Thanks a lot

[ArelyBuzz]

Lefty :)



[patrickJMT]

@ArelyBuzz ftw! : ) 

[MikeyMadness1234]

patrickJMT = Patrick, Jesus My TeacherIsn'tAsSmartAsYouAre. Haha thank you Patrick!!

[patrickJMT]

@MikeyMadness1234 ha, that is what it stands for : )

[xXTheDeathReaperXx]

@patrickJMT I thought it was Jesus Maths Tutor?

[MikeyMadness1234]

@patrickJMT I am alerting everyone on Facebook that you responded to one of my comments on Youtube haha

[patrickJMT]

@MikeyMadness1234 ha!

[iMITCHing]

what about (3i)(2-i) am i just being dumb, i cant get the answer in my book? thanks!

[MrXenitha]

@iMITCHing 3i(2-i), just multiply all the terms in the bracket (2-i) by the coefficient of the bracket; i think you call them parenthesis in America :D.

so, 3i*2 (3i*i)

= 6i + (3i*-i)

= 6i + (3(1))

= 6i + 3

Hope that helps :)

[chacaholly]

thanks!



[TheJphelan]

God Bless you!

Isnt it amazing that some people are just able to understand maths like that?!

last year my teacher couldn't understand why or how we couldn't understand maths and never explained it properly.

Poor teaching performance + lack of care = student confusion and hatred of maths. FACT.

You rock wish I was good at maths :/

[devilfish127]

So patient in explaining all those irritating maths. ;)

[sparkledustpajamas]

You are a lifesaver.

[Naoufalitos24]

great explanation

[coolboyshubham]

♥ly chapter

[MzShawnee100]

, if 3i (2 + 5i) = x + 6i, then x = ?

[TheAncientEmperor]

@MzShawnee100 3i(2+5i)=6i+15i, therefore x=15i, right?

[Cervclash]

can I cancel out if it's like 2+3i/3i?

[MunkikiD]

wat about q's such as "(1+i)^5" ?

[iWriteUinMyDeathNote]

this is the first video i have seen for you. I have to say that you are not a good teacher for those who are beginners because you don't explain anything. But it's good for people who already know how to do it and need a little practice

[zxmco125]

well explained :)

[aligatorsandwitch72]

Guys! Don't believe this bullshit! He isn't really left handed! He is merely writing everything backwards and editing it in movie maker to mirror it! He's a sly one!

[arupsaha1995]

in the second question were u divided the two complex nos.. i was in the denominator..so instead of multipyling the numerator and denominator by i you could have multiplied by i raised to 4..u would hav got answer more easily

[universalSoldier76]

Saved me for my test tomorrow. I think I can get a B+ now (I would have failed without this video). Thanks a lot. I really appreciate when people take their time to help others with their problems.

[PtotheMtotheJ]

I appreciate what you do very much.

[jmsandovalh]

What about 2(5+i)^3 -3(6-2i)^2 i^133=?

I´m confused

[yourmajezty]

great work

[guitar2snow]

Isn't it funny how the best teachers aren't OUR teachers, but people with a love of math on the internet >.<

[12MangoTango34]

This helped a lot , thanks !

Hopefully I can pass my EOCT.

[MicahPrior]

You are the bomb! Thanks for posting these videos...

[ziplockkdweezy]

thank you!!!

[like11whoa]

what if it has the real number on top of the equation like ..... 9/ 7-5i?

[patrickJMT]

@like11whoa multiply by the conjugate

[turtlewax3585]

what about "i" cubed or "i"to the fifth power?!

[patrickJMT]

@turtlewax3585 i^3 = i^2( i ) = (-1)i = -i

[mistymoon67]

I have recently returned to school for upgrading after 25 years. Adult Education does not have teachers, they are considered facilitators. They hand you a book and outline and tell you to go to it. My math book could be Chinese for all the sense it makes! I discovered your tutoring videos when I first started and they have help me learn mathematical Chinese and maintain an above 95% average. So thank you!!

[vjcd4evr]

wow, this helped alot! thank you!

[0wnerFilms300]

thanks, this is probably going to be extra credit on my test tomorrow. Supposidly it is worth 4 points =D wish me luck tomorrow. My teacher totally sucks. He's a sarcastic teacher that looks like an owl.

[Amauri014]

Thanks for make this video, thanks for the help.

[billly728]

i wish he was my teachr 

[patrickJMT]

@billly728 if you watch, i am!

[122Tychell]

@patrickJMT you are a life saver thank you so much :)

[sharifmohamed99]

Thank you thank you thank you thank you :)

[WolfgangNS]

What's i^3 ?

[patrickJMT]

@WolfgangNS -i

[tehn00bpwn3r]

Very useful. You're the most popular guy on Youtube.

[666ferno]

damn you done what no other man or women has ever done before <3

[alreadytakenthe3rd]

You mention late in the video that we for some reason don't want imaginary numbers in our denominator. The reason is that the reciprocal of i is -i. It's slightly unnecessary to multiply by i/i in that last example because you can just split the fraction into 5/i + 6i/i. 6i/i of course reduces to 6, and 5/i turns into -5i if you remember that the reciprocal of i is -i.

[m2komgr]

THANK YOU THANK YOU THANK YOU!!!! Pretty much saved me and yay I love the video thanks a lot!!!!!

[pfifofast]

why does i^2 = -1?

[patrickJMT]

@pfifofast by definition

[yrtsg]

@pfifofast because i = square root of -1 so if you square it the square root goes away leaving the -1

[miguelangel11111]

why you dont conjugate the last exercise by -i

[12Razman21]

left hand writer here :D and ur teaching is amazing keep it up

[Archamity]

left hand writing ftl D:

but your teaching ftw :D

[sssandeep619]

it is nice

[ishhmail]

For the last example why didn't you multiply by the conjugate which would be i squared?

[willable11]

thanks for the videos man, my algebra 2 teacher sucks, you helped me at 3 a.m before a test!

[Theocrooks]

Hey Pat. Thanks again. :) I think you are good at this partly because of your ability to calmly explain things. It might sound weird, but I think I have difficulty learning from this teacher just because of the energy that she puts out and how quickly she goes through stuff. Maybe it's just me. Anyways , thanks for the easily digestable material.

[TheKrazEEe]

at 4:25 just a little mistake that may confuse people. The congugate isnt always found by changing the middle sign + or -. Its changing the sign before the i value.

4-i = 4+i

-i+4 = i+4

[patrickJMT]

@TheKrazEEe ah yes, touche; if the complex number is written in standard form (which is all i use), then what i say is correct. but you are right! thanks

[TheKrazEEe]

@patrickJMT yeah, my calculus teacher often tricks people this way.

[hipaulette]

marry me

[rokkerboi21]

I must say, your videos help me a lot. Thank you very much :)

[patrickJMT]

@rokkerboi21 my pleasure

[Jeralahm]

THANKS

[Wadey456]

This helped a ton! thank you so much

[aggadi]

Thank you

you teach very well and very thanks plz plz keep on posting videos on like this thank you very much sir.patrick.

[crashitbaby17]

i love you patrick<3

[trinigyalwiner]

omg! thank u soo much!!!

[beautifulteaba]

OMG THANK YOU SO MUCH!!!! I HAD NO IDEA ON HOW TO DO THIS IN CLASS BECAUSE I MISSED A DAY THANK GOD I FOUND YOU ... YOUR LIKE HAVING MY OWN TURTOR ON YOUTUBE.

OH AND I SUBSCRIBED TO YOUR CHANNEL NOW AND FOREVER.

THANKS SO MUCH FOR POSTING THIS!!!!!!!

[patrickJMT]

@beautifulteaba no problem ; ) you are very welcome!

[Speechless12886]

YESS!!!!! Now I dont have to cheat on my test!!!!!

Your so GREAT Mr. Patrick!!!!

[tchiriga263]

how do you make it so simple.. cheers mate!

[jeffcrafter]

Thank you...I think I have just foud out how I am going to pass pre-calc

[wierdsince79]

on the last division problem that was done, im a little unclear why the answer was positive instead of negative. 

[KeyanGanjuei]

@wierdsince79 answer may be super late but its because it was already a subtraction, and it was subtracting a negative, resulting in an addition. --=+ basically.

[RedXization]

Thank you sir!

[bizayangdako]

Sr Patrick, do u hav video where i is an exponent of a polar form?

[patrickJMT]

@bizayangdako no, not yet

[bizayangdako]

@patrickJMT oh ok... because I was slightly confused on dealing with i as exponent...

Well thnx for ur videos... it realy helps...

[radday5]

Am in a large class at a community college, and we have been working in complex numbers, and I ended up getting lost. But you helped me throw it thanks so much have a test on this on Monday.

Bill.

[BrandonANDBrantonTV]

it's pretty sad that u explained this better than my teacher.thanks alot, man

[patrickJMT]

@BrandonANDBrantonTV why is that sad? : ) am i just some completely dumb schmuck?!

[BrandonANDBrantonTV]

@patrickJMT no, apparently you're smarter than my teacher lol.last year i had an awesome teacher.this year *shakes head in shame* not so much.thanks alot for the help tho.im sure ill be back lol

[Eniluap010]

dude you are so awesome!

i actually understand this complex thingy.. :D

[MikesIpodHelp]

good thing bout this is although im doing it in further pure, its acually really interedsting and wen u get into it its fun lol :P

[whatisyournam]

thats so good man thanks for that . godbless

[whatisyournam]

thanks man thats so good. godbless

[Nightwalker191]

Wow, I've always wondered how we, as humans, could make up math like this. Talk about really smart people in this world. But it makes me wonder, are we done creating new ways of math, or just getting started?

[patrickJMT]

@Nightwalker191 there are always unsolved problems and new techniques being created. we will never be 'finished' creating new mathematical ideas

[MrVoiceofreason123]

@Nightwalker191 Math is an ongoing process of discovery

[emmycardon]

Thank you so much for helping, but I don't understand why we didn't multiply by the conjugate of i. Is it because it is just i?

[ThugMentality504]

thanks Man Got Some Good Stuff Jusst To Refresh My Mind..

[sklieves]

How do u graph these?

[Charlymaumushi]

The video is great but since he's left handed I can't see what he's righting!

[rosel5693]

Good job! Thank You!

[xAutumnKiss]

u should make guide on logarithms >.> my teacher is bad at explaining

[Mcciiee]

Hey thanks alot patrick , my tets is 2moro , hope it helps ,, . the video is great , its just sometimes u cover the problems with your hands , witch is not a big problem but just saying (=== .. thanks

[Charlymaumushi]

@Mcciiee lol I just posted that too. He's left handed! lol

[candicook08]

wow!!! this is hard

[lajc24]

great way to teach the multiplication and division of complex numbers

[blackroze1000]

Thanx ...... I loved it u made complexed numbers sooo easy

Thank u very much....

[woolbrighttony]

Thanks For The Lesson U Teach Way Better THen My Real Teacher

[NumbNutsxD]

thanks! you're really helpful!

[mileyfan999]

Thank you so so so so so so so much! I have to have eight complex number questions done by tomorrow and I was getting seriously frustrated!

[deceit1991]

This is amazing :D GOOD job!

[dmarcable]

in the last example, is it okay to multiply by -i instead of i?

[Leston7]

@dmarcable yes, it's the same... if you resolve it that way, you'll see that it's the same result, -5i + 6

[TheViideoBug]

You're an amazing teacher!!! Thank youu oh so much!!! :DD THANK YOU!

You make things easy & cut out all the little extra complicated steps. :)

You're my hero. :)

[adrianwright08]

Thanks alot! This post really helped me.

[sarahstarr100]

Thank you honey, you have a talent for explaining things simply, quickly, and clearly! you should really go into teaching. Its very good of you to take your time and donate it in this manner to the world. You have really helped me a lot and decreased my stress about math immensly.

[Jean1juan]

why is it 6 over -1. it should be positive

[TheJosephOuellette]

@Jean1juan i^2 = -1

[01supra]

bust this up lol i like that u make this so easy now thanks man

[XoXoKimberlyy]

Thanks ^^

[fashionmeetpuppy]

OMGGG i have a test tomorrow on all of this and i used your vid to help me study now i know ima pass YAY!!! your the freaking BEST DUDE =D

[reb1271]

Its official my child's name will be patrickJMT

[Chelsea100]

Thank you so much for this, you have no idea how you've helped!

[SAIKOREB0N]

You're my hero!! =D

[JagH8ter]

i love you

[mariohds86]

thank you so much, I'm trying to pass college algebra and your videos are awesome, really helpful!!

[RyuHanamichi]

math is cool!

[XxNaSaHxX]

I'm a lefty too :D LEFTY POWERRRRRRR

[naveenthejustice]

I can't even begin to describe to you how helpful this video was to me. Thank you so much. I have used your math videos so much. It seems as though i m watching my favourit movie

[JImmyandMike16]

Thank you very much, your a huge help!

[OperaEmma]

you are my hero :P thankiess!

[TifDuckie3]

I can't even begin to describe to you how helpful this video was to me. Thank you soooo much. I have used your math videos so much. It seems as though whenever I review for a test using your videos, I pass with flying colors :D

[netskater4454]

First of all, thx so much, i really understand how to this, and my question is, for the last example you showed the answer is -5i+6, i was wondering if i get 6 - 5i, is it still correct? Does it matter where i put the 5i?

[TifDuckie3]

I was told in my math class that it is best to put real numbers in the front. So in your scenario,

6 - 5i is correct. It would be the better answer.

[st335533]

if i pass my math test today, im totally gona nominate you for nobel peace prize

[DarkfairyCT]

Thank you so much for making this helpful video!!!!

[surfsnakes]

You're an absolute legend, its quite easy if you get it from someone who actually likes to teach.

Thank you

[livin4pussy]

wow dude your a great teacher.

[Tilex1990]

thanks. now i got, even tho i'm not a native speaker =)

[123silvia]

This video really helped:)

Thank You!

[kimyuie]

I UNDERSTAND NOW! :D

Thanks so much, now I don't think I'll fail my test.

[atomo360]

thanks agian sr.patrick!

[SaxxItUp]

Seriously, you just saved my life (not really.) I was sitting here ripping my hair out trying to figure out these stupid things. Thank God I youtubed. THANK YOU SO MUCH FOR THIS.

[QuantumMaths]

You should go into complex analysis :))

[doncharchar]

You just saved me a lots of time. You're a cool guy.

[Noold]

Could you do some more examples on dividing the Complex numbers? harder to do basically? so i can work it out ..