In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, field theory, and the discrete Fourier transform.
The notion of root of unity also applies to any algebraic ring with a multiplicative identity element, namely a root of unity is any element of finite multiplicative order.
Read more about Root Of Unity: Definition, Elementary Facts, Examples, Periodicity, Summation, Orthogonality, Cyclotomic Polynomials, Cyclic Groups, Cyclotomic Fields, Root of Unity in Finite Fields
Famous quotes containing the words root and/or unity:
“Better extirpate the whole breed, root and branch. And this, unless the German people come to their senses, is what we propose to do.”
—Gertrude Atherton (1857–1948)
“Hearing, seeing and understanding each other, humanity from one end of the earth to the other now lives simultaneously, omnipresent like a god thanks to its own creative ability. And, thanks to its victory over space and time, it would now be splendidly united for all time, if it were not confused again and again by that fatal delusion which causes humankind to keep on destroying this grandiose unity and to destroy itself with the same resources which gave it power over the elements.”
—Stefan Zweig (18811942)