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

1. ## 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?

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

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

3. ## 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

4. ## 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: $z=\cot \left(\frac{2m+1}{14}\pi \right)$

5. ## 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...