Explore BrainMass

Explore BrainMass

    DeMoivre's Theorem - Euler Form

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file.

    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 8:32 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/demoivre-s-theorem-euler-form-175367

    Attachments

    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.

    $2.49

    ADVERTISEMENT