The 
th roots of unity are roots 
of the cyclotomic
equation
 |
which are known as the de Moivre numbers. The notations 
,
, and 
, where the value of 
is understood by context, are variously used to denote the
th 
th root of unity.
is always an 
th root of unity, but 
is such a root only if 
is even. For 
, the roots of unity form a regular
polygon with 
polygon edges, and each polygon
vertex lies on the unit circle.
The roots of unity belonging to the number field 
generated by an algebraic
number 
are returned by the Wolfram Language
function NumberFieldRootsOfUnity[a].
