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. In general, the roots of unity form a regular
polygon with 
sides, and each vertex lies on the unit circle.
