# RootOfUnityQ

RootOfUnityQ[a]

yields True if a is a root of unity, and yields False otherwise.

# Details

• An algebraic number a is a root of unity if an=1 for some integer n.

# Examples

open allclose all

## Scope(5)

Root objects:

AlgebraicNumber objects:

Transcendental objects:

## Properties & Relations(4)

Roots of unity are solutions of for some integer n:

All roots of unity are algebraic integers that lie on the unit circle:

Not all algebraic numbers on the unit circle are roots of unity:

The minimal polynomial of a root of unity is a cyclotomic polynomial or one of its factor:

Roots of cyclotomic polynomials are roots of unity:

Use NumberFieldRootsOfUnity to find all roots of unity in a number field:

## Possible Issues(1)

Approximate numbers will always return False:

Use RootApproximant to get an exact number:

Wolfram Research (2007), RootOfUnityQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RootOfUnityQ.html.

#### Text

Wolfram Research (2007), RootOfUnityQ, Wolfram Language function, https://reference.wolfram.com/language/ref/RootOfUnityQ.html.

#### CMS

Wolfram Language. 2007. "RootOfUnityQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RootOfUnityQ.html.

#### APA

Wolfram Language. (2007). RootOfUnityQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootOfUnityQ.html

#### BibTeX

@misc{reference.wolfram_2023_rootofunityq, author="Wolfram Research", title="{RootOfUnityQ}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RootOfUnityQ.html}", note=[Accessed: 22-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_rootofunityq, organization={Wolfram Research}, title={RootOfUnityQ}, year={2007}, url={https://reference.wolfram.com/language/ref/RootOfUnityQ.html}, note=[Accessed: 22-April-2024 ]}