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Let $z$ be a complex number such that $z^5 = 1$ and $z \neq 1.$ Compute \[z + \frac{1}{z} + z^2 + \frac{1}{z^2}.\]

 Aug 1, 2020
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We can solve, to get z = 0.951057 + 0.309017*i.  Then z + 1/z + z^2 + 1/z^2 = -3.

 Aug 1, 2020

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