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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!

 Sep 2, 2019
edited by Davis  Sep 7, 2019
edited by Davis  Sep 7, 2019
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n  =  zero

z  =  anything except zero

.

 Sep 3, 2019
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What about complex numbers? Sorry, I did not make it clear that \(z\) could be a complex number. Thanks!

Davis  Sep 7, 2019

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