### What does **root of unity** mean?

# Definitions for root of unity

root of uni·ty

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **root of unity**.

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### Wikipedia

Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. 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. Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple of the (positive) characteristic of the field.

### Freebase

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 integer power n. 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 n nth roots of unity, if n is not divisible by the characteristic of the field.

### Numerology

Chaldean Numerology

The numerical value of root of unity in Chaldean Numerology is:

**7**Pythagorean Numerology

The numerical value of root of unity in Pythagorean Numerology is:

**7**

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"root of unity." *Definitions.net.* STANDS4 LLC, 2023. Web. 8 Dec. 2023. <https://www.definitions.net/definition/root+of+unity>.

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