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:
“Perhaps the whole root of our trouble, the human trouble, is that we will sacrifice all the beauty of our lives, will imprison ourselves in totems, taboos, crosses, blood sacrifices, steeples, mosques, races, armies, flags, nations, in order to deny the fact of death, which is the only fact we have.”
—James Baldwin (1924–1987)
“Flower in the crannied wall,
I pluck you out of the crannies,
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.”
—Alfred Tennyson (1809–1892)
“The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
—Ralph Waldo Emerson (1803–1882)