Principal Root of Unity

A principal th root  of unity is a root satisfying the equations  and

for , 2, ..., . Therefore, every primitive root of unity of fixed degree  over a field is a principal root of unity, although this is not in general true over rings (Bini and Pan 1994, p. 11).

Informally, the term "principal root" is often used to refer to the root of unity having smallest positive complex argument.

REFERENCES:

Bini, D. and Pan, V. Polynomial and Matrix Computations, Vol. 1: Fundamental Algorithms. Boston, MA: Birkhäuser, 1994.