The roots of $z^6+z^4+z^2+1=0$ are the vertices of a convex polygon in the complex plane.  Find the sum of the squares of the side lengths of the polygon.
Question:
The roots of $z^6+z^4+z^2+1=0$ are the vertices of a convex polygon in the complex plane.  Find the sum of the squares of the side lengths of the polygon.
Answer:
Let's think step by step.

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12 - 4 \sqrt{2}
The roots of $z^6+z^4+z^2+1=0$ are the vertices of a convex polygon in the complex plane.  Find the sum of the squares of the side lengths of the polygon.
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