olymmath

HMMT 2009 U23

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The roots of z6+z4+z2+1=0z^{6}+z^{4}+z^{2}+1=0 are the vertices of a convex polygon in the complex plane. Find the sum of the squares of the side lengths of the polygon.

Dataset text NuminaMath olympiads. Quoted with source.

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12-4 \sqrt{2}

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