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 of, root and/or unity:
“The love of money is the root of all evil.”
—Bible: New Testament St. Paul, in 1 Timothy, 6:10.
“The root of the discontent in American women is that they are too well educated.... There will be no real content among American women unless they are made and kept more ignorant or unless they are given equal opportunity with men to use what they have been taught. And American men will not be really happy until their women are.”
—Pearl S. Buck (1892–1973)
“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)