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.

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