Principal Root of Unity

A principal 👁 n
th root 👁 omega
of unity is a root satisfying the equations 👁 omega^n=1
and

for 👁 j=1
, 2, ..., 👁 n
. Therefore, every primitive root of unity of fixed degree 👁 n
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.

See also

Primitive Root of Unity, Principal Square Root, Root of Unity

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References

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

Referenced on Wolfram|Alpha

Principal Root of Unity

Cite this as:

Weisstein, Eric W. "Principal Root of Unity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrincipalRootofUnity.html

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