RootOfUnityQ
RootOfUnityQ[a]
yields True if a is a root of unity, and yields False otherwise.
Examples
open all close allBasic Examples (1)
Scope (5)
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:
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