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Math Help - Algebraic Application invovling de Moivre's Therom

  1. #1
    Junior Member
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    Mar 2007
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    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.
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  2. #2
    Senior Member
    Joined
    Dec 2007
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    It might help to write -1 as -1+0i. Then just use:

    <br />
|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.
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