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De Moivre Theorem - explanation of roots! watch

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    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.
    Could someone please explain ?

    Thanks so much
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    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?
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    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.
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    This pic should explain
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    (Original post by SubAtomic)
    This pic should explain
    Thanks! Which book is this btw?
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    (Original post by Sifr)
    Thanks! Which book is this btw?
    np. Edexcel FP2
 
 
 
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Updated: March 18, 2013
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