Originally Posted by

**niaren** I could need a hint on how to find all solutions to this equation

$\displaystyle \left( \frac{1+z^{-1}}{1+z} \right)^N = C$

where C is a real constant, N is a positive integer, and and z is the complex variable. I'm not sure I can just write

$\displaystyle \frac{1+z^{-1}}{1+z} \right = C^{1/N}$. It should probably look more like $\displaystyle \frac{1+z^{-1}}{1+z} \right = C^{1/N}e^{2\pi i k/N}$, for $\displaystyle k=0,1,...N-1$.

But then I'm unsure as how to proceed. I have tried writing z in polar form but it didn't give me a break through.