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    DeMoivre's Theorem - Euler Form

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    1) Express each of the following as a complex number in the Euler form z = r e^ftheta or using the phasor notation z = r <theta
    [which is an abbreviation for the pola form z = r(cos theta + j sin theta) J:

    a. ((square root 3) - j)(1 + j(square root 3))) / (1 - j)
    b. square root(12 - 9j) (principal square root only)

    2) a) Use deMoivre's Theorem to express tan 4theta in the form of a ratio of functions which involve powers of tan theta;

    b) Show that j^j = (square root - 1)^(square root - 1) is real and find its principal value.

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    Solution Summary

    The following solution shows how to express complex numbers in Euler form and uses deMoivre's theorem to solve. The solution is enclosed within a .zip file which is attached.