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Math Help - Find all the complex solutions

  1. #1
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    Find all the complex solutions

    z^7 - i = 0

    the answer need to be in polar form between - pie to pie.

    Thank you in advance
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  2. #2
    MHF Contributor red_dog's Avatar
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    z^7=i\Rightarrow z^7=\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}

    Then, z_k=\cos\frac{\frac{\pi}{2}+2k\pi}{7}+i\sin\frac{\  frac{\pi}{2}+2k\pi}{7}, \ k=0,1,\ldots ,6
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