Polygon From Complex Roots
Algebra
Level
3
Consider the following equation:
\(x^{5}=-1\)
Suppose that all of the unique roots of this equation are plotted as points in the complex plane. These points are then connected with straight lines to form a convex polygon that is symmetrical with respect to the real axis. Determine the perimeter of the polygon.
Give your answer to 3 decimal places.
by
Steven Chase