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    Solving Complex Variable Equations : DeMoivre's Theorem

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    Find the values of:


    The answer is:

    cos(pi*sqrt(3)[1/2+2k]) + i.sin(pi*sqrt(3)[1/2+2k]), for any integer k.

    keywords: de moivres, de moivre's

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    Solution Preview

    this is a neat application of de moivre's formula; indeed, this should remind you of how to extract roots of complex numbers! as a first step you would need to write the base of the exponent in polar form, so

    i = 0 + 1i = cos (pi/2) + i sin (pi/2)

    but the effect of ...

    Solution Summary

    De Moivre's theorem is applied. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.