Root of Unity

The $n$th Roots of Unity are Roots $\zeta_k=e^{2\pi ik/n}$ of the Cyclotomic Equation

$$x^n=1,$$

which are known as the de Moivre Numbers.

See also Cyclotomic Equation, de Moivre's Identity, de Moivre Number, Unity

References

Courant, R. and Robbins, H. ``De Moivre's Formula and the Roots of Unity.'' §5.3 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 98-100, 1996.