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Root of unity

The roots of unity (or de Moivre numbers) are all complex numbers that yield 1, when they are elevated to a given power n.



The roots roots of unity lie on the unit circle of the complex plane and they form in that complex plane n-sided regular polygons with a vertex at 1. These are the solutions of the equation

z n = 1

where n is a natural number. The solutions are the points on the unit circle (circle with radius 1 around the origin) given in polar form by

zk = e 2π i k / n


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