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:
“At the root of all these noble races, the beast of prey, the splendid blond beast prowling greedily in search of spoils and victory, cannot be mistaken.”
—Friedrich Nietzsche (1844–1900)
“And a man of tan engages
For the springtime of her pride,
Eats the green by easy stages,
Nibbles at the root beneath
With intimidating teeth.”
—Gwendolyn Brooks (b. 1917)
“As the unity of the modern world becomes increasingly a technological rather than a social affair, the techniques of the arts provide the most valuable means of insight into the real direction of our own collective purposes.”
—Marshall McLuhan (1911–1980)