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:
“Evil being the root of mystery, pain is the root of knowledge.”
—Simone Weil (1909–1943)
“...there is hope for a tree, if it is cut down, that it will sprout again, and that its shoots will not cease. Though its root grows old in the earth, and its stump dies in the ground, yet at the scent of water it will bud and put forth branches like a young plant. But mortals die, and are laid low; humans expire, and where are they?”
—Bible: Hebrew, Job 14:7-10.
“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)