Root of Unity

The th roots of unity are roots of the cyclotomic equation

which are known as the de Moivre numbers. The notations , , and , where the value of is understood by context, are variously used to denote the th th root of unity.

is always an th root of unity, but is such a root only if is even. In general, the roots of unity form a regular polygon with sides, and each vertex lies on the unit circle.

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