Polygon From Complex Roots

Algebra Level 3

Consider the following equation:

x 5 = − 1 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.


The answer is 5.878.

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Steven Chase by Steven Chase , 37, USA

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1 solution

Steven Chase
Jul 31, 2016

2 Helpful 1 Interesting 1 Brilliant 0 Confused

For most of America, 200k is a very good salary. In coastal cities in California, it's much more expensive, so 200k doesn't go as far.

Steven Chase - 10 months, 1 week ago

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