This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

RootOfUnityQ

RootOfUnityQ[a]
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.
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
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:
New in 6