Let $z$ be a complex number such that $z^5 = 1$ and $z \neq 1.$ Compute \[z + \frac{1}{z} + z^2 + \frac{1}{z^2}.\]
We can solve, to get z = 0.951057 + 0.309017*i. Then z + 1/z + z^2 + 1/z^2 = -3.
