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.
“But a cultivated man becomes ashamed of his property, out of new respect for his nature. Especially he hates what he has if he see that it is accidental,—came to him by inheritance, or gift, or crime; then he feels that it is not having; it does not belong to him, has no root in him and merely lies there because no revolution or no robber takes it away.”
—Ralph Waldo Emerson (1803–1882)
“Jesus abolished the very concept of “guilt”Mhe denied any cleavage between God and man. He lived this unity of God and man as his “glad tidings” ... and not as a prerogative!”
—Friedrich Nietzsche (1844–1900)