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Math Help - Urgent Complex Number Multiple Choice Question Help

  1. #1
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    Urgent Complex Number Multiple Choice Question Help

    Let z=1024i, which of the following represents all the solutions of w = z^(1/5)?

    a) 4e^(itheta), theta = pi/10, pi/2, 9pi/10, 13pi/10, 17pi/10
    or
    b) 4e^(itheta), theta = pi/10, 3pi/10, pi/2, 7pi/10, 9pi/10

    Thank you!
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  2. #2
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    Quote Originally Posted by ComplexNumbers101 View Post
    Let z=1024i, which of the following represents all the solutions of w = z^(1/5)?

    a) 4e^(itheta), theta = pi/10, pi/2, 9pi/10, 13pi/10, 17pi/10
    or
    b) 4e^(itheta), theta = pi/10, 3pi/10, pi/2, 7pi/10, 9pi/10

    Thank you!
    In polar form

    z=2^{10}e^{i\frac{\pi}{2}}

    z^{\frac{1}{5}}= 2^2e^{i\frac{\pi}{10}}

    The rest of the roots are evenly spaced around the circle by

    \frac{2\pi}{5}=\frac{4\pi}{10} radians
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