What is "root of unity"

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power . Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform.

In field theory and ring theory the notion of root of unity also applies to any ring with a multiplicative identity element. Any algebraically closed field has exactly th roots of unity if is not divisible by the characteristic of the field.