HMMT 2010 A5

Suppose that $x$ and $y$ are complex numbers such that $x+y=1$ and that $x^{20}+y^{20}=20$ . Find the sum of all possible values of $x^{2}+y^{2}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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1, -1, i, -i

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