(z+i)^7 + (z-i)^7 =0? How do I find the complex roots?
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Originally Posted by anom88 (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.
I got some help and was shown that it boils down to cot(((2m+1)/14)pi) for m=0...6
$\displaystyle \left(\frac{z+i}{z-i}\right)^7=-1 $ $\displaystyle \frac{z+i}{z-i}=-e^{i 2m \pi /7}$ $\displaystyle m=0,...,6$ answer: $\displaystyle z=\cot \left(\frac{2m+1}{14}\pi \right)$
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...