De Moivre's Theorem

[Deepskies1]

what's the music played please 

[69uselessacount]

thanks helped a lot(:

[HeroDefender]

Can't be said enough, your penmanship is remarkable!

[ANILTHEGAME]

SILENCE IS THE KEY OF SUCCESS!!

Awesome hand writing bro~

[CantCreat]

a w/e the cos is 1. my bad :D tnx for upload

[CantCreat]

isn't the answer -4096 coz cos(8pi)=-1 and isin(8pi)=0 => 4096*-1= - 4096. plz correct me if i am mistaken

[stargirllilac]

hey y is the answer just 4096 in the end? and how'd he get the angle as 2pi/3?

[Calculus117]

there is any error you made with the angel it should be -60 or -2pi/3 draw the diagram and work it out

[ivasenko48]

@Calculus117 true, but cos(-2pi/3)=cos(2pi/3) and sin (-2pi/3)=sin(2pi/3) so what he wrote it still correct.

[reginaldcosio]

you didn't show how to get the theta. You just copied it straight from the precal with limits, huh?

[Pilotman1992]

I understood in silence

[DarrenM813]

he may not have talked to explain but this was a far better de moivres explanation than anywhere else on youtube

[pollardrho06]

@DarrenM813 : Thanks Darren!!

[chris9232]

ty man



[kungman190]

I can NOT understand why mixing music with maths!!!!!!!!

[the9dolls]

Beautiful. So does it have 12 roots?

[sheepshitonastick]

Please Answer...

Why Do You Multiply It By 2?

PLEASE ANSWER IT WOULD HELP ALOT!

Thanks.

[the9dolls]

@sheepshitonastick

Have a look at Polar Coordinates-The Basics. It is the value or r. You perhaps have found it already. Anyway, good luck.

[YahZozo]

@sheepshitonastick

the 2 was that he found the modules the r which is r = root (x^2+y^2) then he found angle by tan^-1(y/x)

if you do it you get = root (1^2 + (root 3)^2) = 2

hope that helps :)

[8o8ThaiSoul]

music made me depressed... Lol

[Lavabug]

I understand the theorem but not the example, where does the coefficient 2 (and 2pi/3 in the trig arguments) come from?

[annapurple18]

how did you get the two if you dont mind ??

[asolutionforyou]

if you understand spanish see in youtube watch?v=LS6y8hOUPwY&feature=re­lated

juanmemol explain It also (and more of a thousand riles of maths also)

[godspeed28]

pro tip, pick a good song, mute video and play. nice handwriting btw

[yesungscloud]

lol@ the song in the beginning.

to me, de moivre's theorem is scarier than

the scariest movie there is.

[elizze6]

I don't understand the example

[toda9008]

how do you solve z to the 8th power equal 1. I know how to set it up but I'm having trouble find r and the angle (theta)

[nourchaalan]

What a nice hand writting!!!!!!!!!!!

[pollardrho06]

@nourchaalan Thanks :-)

[lovely2626]

@pollardrho06 you should explain how you getting the information

[fairyskies]

Thank you so much! You're awesome!

[pollardrho06]

@fairyskies You're very welcome!

[ChevronShifter]

How did you choose 2pi/3 for the value of theta?

[Yu2Kal]

Cos 2pi/3 = -1/2

iSin 2pi/3 = i(root 3 ) / 2

Then as you can see there is a value of 2 outside the brackets so when you bring it in it becomes -1 + root 3i its the same thing he just re wrote it

[ChevronShifter]

So did he choose 2pi/3 using arctan(negative rad3)?

[Yu2Kal]

Lol, dude I think you've lost the plot, all he did was that he re wrote it to simplfy the problem

[ChevronShifter]

I see that when you perform the trig. operations and multiply by two you get the original term. But looking at it that way is inductive reasoning. There's no clear way (presented here) to find the value of theta in any general case.

[Yu2Kal]

I think I understand what you mean, your asking how and why he chose the value of theta?

[ChevronShifter]

That is precisely what I am asking.

[Yu2Kal]

Its just the simplest value which keeps the equation true, he could have used 8pi/3 if he wanted to, but why complicate matters.

[zacatara]

awesome dude! really helpful! why don't the lecturers just say so!?!

[stockshunter]

do a rigirous proof of basel problem that involves De Moivre's theorm

[webmeba]

oh and what's the music mate :-) ?

[candy4annie]

what i am confused on is how do you get the 2 in front of the brackets!!!! i am so confused on that but everything else i understand .. id apprecaite it alot if ou could answer that westion for me thatnks

[coldheartedrose]

the r : is the 2 which you solve by doing Square root ( X^2+y^2) kind of like pythagorean thm. let x be Sqrt(3) and y be -1= Sqrt (4) >>> 2 hope that helps!!

[emopinay]

hi there, i was wondering, how can you solve this with de moivre's theorem? [3(rad 2- rad 2i)]^4 appreciate it if you help me out =)

[pollardrho06]

No problem. Will post the solution to that in a little while.

[mizzbanks707]

i'm in pre-calculus and i've been having problems with this and thank u for posting this...but i do have a few questions... how did you go from 2pi/3 to 8pi? i'm assuming that the 2pi/3 comes from tan theta= b/a which would be negative root 3 this theorem always gives me trouble pleas reply; once again thanks soooo much for posting

[pollardrho06]

Hey there. No problem at all. Thanks for the appreciation...

Here's answering your question...

how did you go from 2pi/3 to 8pi?

The exponent/power of 12 multiplies the 2pi/3 to give 24pi/3 which is equal to 8pi. We are able to do this becuase of De Moivre's Theorem.

Hope this helps. If there is still room for confusion feel free to e-mail me. Will send you an e-book free of cost on complex numbers that'll help you ace pre-calc.

Best of luck.

[mizzbanks707]

THANK you soooooooo much!!!!!!!!!!!!!

[pollardrho06]

Anytime... :-)

[VeritySeeker]

Good work, mate. Wish I could make my videos writing with my hand, but my handwriting kind of stinks. ;)

[pollardrho06]

Thanks buddy.

[gellybelly2]

Thanks for the post

[pollardrho06]

You're very welcome my friend. Also, your suggestions have been recorded and will be up here in a day or two...

Keep watching...

Shahz.