Find all possible integer values of \(z\) such that the following system of equations has a solution for \(z\): \(\begin{align*} z^n &= 1, \\ \left(z + \frac{1}{z}\right)^n &= 1. \end{align*}\)
Edit: \(z\) can be a complex number, too!
n = zero
z = anything except zero
.
What about complex numbers? Sorry, I did not make it clear that \(z\) could be a complex number. Thanks!
+501 
