# Algebraic Application invovling de Moivre's Therom

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• Mar 17th 2008, 10:39 PM
holmesb
Algebraic Application invovling de Moivre's Therom
I don't really understand some examples I have been working through in finding the roots of complex numbers. One of the examples I am encountering problems with is:

z^6= -1

I am aware that I have to use the formula:

w = (mod z)^1/n cis ((theta + 2kpi)/n).

If I could get a quick worked example it would be much appreciated.

Edit: I think the main problem i am having finding the values for mod z and theta and not actually applying the formula.
• Mar 17th 2008, 11:28 PM
badgerigar
It might help to write -1 as -1+0i. Then just use:

$
|z| = \sqrt{ Re(z)^2+Im (z)^2}$

$\theta = \arg(z) = \arctan(\frac {Im(z)}{Re(z)})$
You will need to ensure that the angle is in the correct quadrant.