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Math Help - Complex Numbers Question

  1. #1
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    Complex Numbers Question

    I've been having problems with this question - it's simple enough to solve, just that I don't seem to get the provided answers (which I suspect might be wrong).

    Find the roots of (z - 2i)^5 = 1

    The answers given are
    root(3/2) +/- 3/2 i,
    root(3) - 3/2 i
    [root(3/2) - 3] + 3i

    Yes apparently there are only 4 roots given, is there something seriously wrong with the answers provided?

    Many thanks.
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  2. #2
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    Quote Originally Posted by h2osprey View Post
    I've been having problems with this question - it's simple enough to solve, just that I don't seem to get the provided answers (which I suspect might be wrong).

    Find the roots of (z - 2i)^5 = 1

    The answers given are
    root(3/2) +/- 3/2 i,
    root(3) - 3/2 i
    [root(3/2) - 3] + 3i

    Yes apparently there are only 4 roots given, is there something seriously wrong with the answers provided?

    Many thanks.
    Let \zeta = \cos \frac{2\pi}{5}+i\sin \frac{2\pi}{5}.
    Then the solutions for z are: 2i+1,2i+\zeta,2i+\zeta^2,2i+\zeta^3,2i+\zeta^4.
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  3. #3
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    Yup I got those answers too - I'm assuming the provided answers are wrong then?
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  4. #4
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    Quote Originally Posted by h2osprey View Post
    I'm assuming the provided answers are wrong then?
    They are wrong. You can just substitute them into the equation and see they fail.
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