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Thread: Trying to find the complex roots, but can't figure it out

  1. #1
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    Trying to find the complex roots, but can't figure it out

    (z+i)^7 + (z-i)^7 =0? How do I find the complex roots?
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  2. #2
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    Re: Trying to find the complex roots, but can't figure it out

    Quote Originally Posted by anom88 View Post
    (z+i)^7 + (z-i)^7 =0? How do I find the complex roots?
    There is no nice way to find these roots. Look Here.

    Also here
    & here
    Last edited by Plato; Mar 17th 2017 at 09:28 AM.
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  3. #3
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    Re: Trying to find the complex roots, but can't figure it out

    I got some help and was shown that it boils down to cot(((2m+1)/14)pi) for m=0...6
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    Re: Trying to find the complex roots, but can't figure it out

    \left(\frac{z+i}{z-i}\right)^7=-1

    \frac{z+i}{z-i}=-e^{i 2m \pi /7}

    m=0,...,6

    answer: z=\cot \left(\frac{2m+1}{14}\pi \right)
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  5. #5
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    Re: Trying to find the complex roots, but can't figure it out

    Of course you would also need to check that z = i is not a root, so that you know you're not dividing by 0...
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