### A Complex Problem

Given a regular n-gon P1P2…Pn. Let point O be the center of this polygon. If we take arbitrary point P in the plane, prove that |PP1|2+|PP2|2+|PP3|2+…+|PPn|2 = n|PO|2+n.

Hint: Complex numbers make this problem easier!

Given a regular n-gon P1P2…Pn. Let point O be the center of this polygon. If we take arbitrary point P in the plane, prove that |PP1|2+|PP2|2+|PP3|2+…+|PPn|2 = n|PO|2+n.

Hint: Complex numbers make this problem easier!