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 bud of the apple is desire, the down-falling gold,
The catbird’s gobble in the morning half-awake
These are real only if I make them so. Whistle
For me, grow green for me and, as you whistle and grow green,
Intangible arrows quiver and stick in the skin
And I taste at the root of the tongue the unreal of what is real.”
—Wallace Stevens (1879–1955)
“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)
“From cradle to grave this problem of running order through chaos, direction through space, discipline through freedom, unity through multiplicity, has always been, and must always be, the task of education, as it is the moral of religion, philosophy, science, art, politics and economy; but a boy’s will is his life, and he dies when it is broken, as the colt dies in harness, taking a new nature in becoming tame.”
—Henry Brooks Adams (1838–1918)