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    Finding all complex fourth roots

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    Find all complex fourth-roots in rectangular form of

    w= 121 ( cos 2pi/3 + i sin 2pi/3 )

    Type answer in the form a + bi round to the nearest tenth.

    Zsub 0 = ? + ?i
    Zsub 1 = -? + ?i
    Zsub 2 = -? - ?i
    Zsub 3 = ? - ?i

    © BrainMass Inc. brainmass.com March 4, 2021, 11:39 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/demoivres-theorem-complex-roots-443657

    Solution Preview

    If we write the solution of z^4 = w as:

    z = r [cos(theta) + i sin(theta)]

    then the equation becomes:

    r^4 [cos(4 theta) + i sin(4 theta) ] = 121 [ cos(2pi/3) + i sin(2pi/3) ]

    This then implies that:

    r = 121^(1/4) = sqrt(11)

    and

    4 theta = 2 ...

    Solution Summary

    We show how DeMoivre's Theorem can be used to compute all the fourth roots of a number.

    $2.49

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