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# De Moivre Theorem - explanation of roots! watch

1. Hi so I havnt done any proper maths for a while and was refreshing over De Moivre's Theorum

I understand the basic concept & formula, but came across this in my notes:

http://i1352.photobucket.com/albums/...psca26f208.jpg

For the life of me I can't work out how they got these roots.

Thanks so much
2. My main issue is I'm so used to

z = e^(i.ø) = cosø + isinø
z^n = e^(i.ø.n) = cos(nø) + isin(nø)

How do I use this to find roots, or how is this used for the above roots stuff I've shown?
3. You start from the first one, so cos0 + isin0 and add 2pi/n where n is the number of roots you want to find. n=4 here so you add 2pi/4=pi/2 to the angle every time to find the roots.

So the angle at the start is 0 and it cycles through pi/2, pi, 3pi/2, 2pi (which is equal to 0). These different angles can be plugged into cos(theta)+isin(theta) to find the values of the roots in the form a+bi.
4. This pic should explain
Attached Images

5. (Original post by SubAtomic)
This pic should explain
Thanks! Which book is this btw?
6. (Original post by Sifr)
Thanks! Which book is this btw?
np. Edexcel FP2

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