This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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yields True if a is a root of unity, and yields False otherwise.
  • An algebraic number a is a root of unity if for some integer n.
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Radical expressions:
Root objects:
Transcendental objects:
RootOfUnityQ threads automatically over lists:
Roots of unity are solutions of for some integer :
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 factors:
Roots of cyclotomic polynomials are roots of unity:
Use NumberFieldRootsOfUnity to find all roots of unity in a number field:
Approximate numbers will always return False:
Use RootApproximant to get an exact number:
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