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# De Moivre's Theorem

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1. Hi Guys,

I've got stuck on question 1b on this problem sheet - see attached pics. I've also uploaded the answers as well.

I see that there should be 4 roots as you have w^2, so youll have a plus and minus version of w which in itself will have two roots, like in question 1a. However from my working out i get ((2^1/2)/2 + (i(5^1/2))/2) as one of them for example so have no idea how they introduced exponential's into there answers.

Any help would be appreciated.

Cheers
Attached Images

2. (Original post by trm1)
Hi Guys,

I've got stuck on question 1b on this problem sheet - see attached pics. I've also uploaded the answers as well.

I see that there should be 4 roots as you have w^2, so youll have a plus and minus version of w which in itself will have two roots, like in question 1a. However from my working out i get ((2^1/2)/2 + (i(5^1/2))/2) as one of them for example so have no idea how they introduced exponential's into there answers.

Any help would be appreciated.

Cheers
The exponential form of a complex number...
3. (Original post by zetamcfc)
The exponential form of a complex number...
I've not come across that yet...?

After looking it up, are you referring to this:

z=re^i(theta)?
4. (Original post by trm1)
I've not come across that yet...?

After looking it up, are you referring to this:

z=re^i(theta)?
Yes, may I ask why you are doing these question if you have not come across this fact?
5. (Original post by zetamcfc)
Yes, may I ask why you are doing these question if you have not come across this fact?
Dunno, im gunna ask my lecturer' and ill get back to you

Ohhh but just looking over it i can see where it comes from:

weve gone through e^i(theta) = cos(theta) + i sin(theta) before.

As z = r(cos(theta) + i sin(theta)) - polar form of a complex number

then z = re^i(theta)...

i just didnt spot the link and we've never expressed roots in terms of exponentials before.

Cheers mate
6. (Original post by trm1)
Dunno, im gunna ask my lecturer' and ill get back to you

Ohhh but just looking over it i can see where it comes from:

weve gone through e^i(theta) = cos(theta) + i sin(theta) before.

As z = r(cos(theta) + i sin(theta)) - polar form of a complex number

then z = re^i(theta)...

i just didnt spot the link and we've never expressed roots in terms of exponentials before.

Cheers mate
All good
7. (Original post by zetamcfc)
All good
I've attached my working, i seem to have got the first of the four roots correct, but the second one I get 4/3Pi not 2/3Pi, but i cant see where ive gone wrong?
Attached Images

8. (Original post by trm1)
I've attached my working, i seem to have got the first of the four roots correct, but the second one I get 4/3Pi not 2/3Pi, but i cant see where ive gone wrong?
4/3 pi = -2/3 pi
9. (Original post by zetamcfc)
4/3 pi = -2/3 pi
Whilst I know what you mean this statement hurt my eyes...
10. (Original post by IrrationalRoot)
Whilst I know what you mean this statement hurt my eyes...
Easiest way to get the point across.

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