# 2007 UNCO Math Contest II Problems/Problem 8

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## Problem

A regular decagon $P_1P_2P_3\cdots P_{10}$ is drawn in the coordinate plane with $P_1$ at $(2,0)$ and $P_6$ at $(8,0)$. If $P_n$ denotes the point $(x_n ,y_n )$, compute the numerical value of the following product of complex numbers: $( x_1+iy_1)( x_2+iy_2)( x_3+iy_3) \cdots (x_{10} + iy_{10})$ where $i^2 = -1$ as usual.

$[asy] draw(polygon(10),dot); draw((-2,0)--(2,0),black); draw((-5/3,-2)--(-5/3,2),black); MP("P_1",(-1,0),NW);MP("(2,0)",(-.9,0),SW); MP("P_6",(1,0),NE);MP("(8,0)",(.9,0),SE); [/asy]$