nth root of unity

The nth roots of unity are roots e^(2π i k/n) of the cyclotomic equation x^n = 1, which are known as the de Moivre numbers. The notations ζ_k, ϵ_k, and ε_k, where the value of n is understood by context, are variously used to denote the kth nth root of unity. +1 is always an nth root of unity, but -1 is such a root only if n is even. In general, the roots of unity form a regular polygon with n sides, and each vertex lies on the unit circle.

cyclotomic equation | cyclotomic polynomial | de Moivre number | de Moivre's identity | nth root | primitive root of unity | principal root of unity | unit | unity