Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive 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, and the discrete Fourier transform. In field theory and ring theory the notion of root of unity also applies to any ring with a multiplicative identity element. Any algebraically closed field has exactly n nth roots of unity if n is not divisible by the characteristic of the field.
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Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive 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, and the discrete Fourier transform. In field theory and ring theory the notion of root of unity also applies to any ring with a multiplicative identity element. Any algebraically closed field has exactly n nth roots of unity if n is not divisible by the characteristic of the field.
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1の冪根（いちのべきこん、英: root of unity） ...... 、または1の原始累乗根（いちのげんしるいじょうこん）という。
@ja
Em matemática, as raízes n-ési ...... z quarta primitiva da unidade.
@pt
En matemática, las raíces n-és ...... dicho plano, siempre que n>2.
@es
En mathématiques, une racine d ...... lique dans le cas d'un anneau.
@fr
In de wiskunde zijn voor een g ...... lhoeken met een hoekpunt op 1.
@nl
In der Algebra werden Zahlen, ...... , -te Einheitswurzeln genannt.
@de
In matematica, le radici -esim ...... o le soluzioni dell'equazione:
@it
In mathematics, a root of unit ...... e characteristic of the field.
@en
Pierwiastek z jedynki n-tego s ...... że być w szczególności ciało .
@pl
Корни n-й степени из единицы — ...... инейкой, представлениях групп.
@ru
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1の冪根（いちのべきこん、英: root of unity） ...... 、または1の原始累乗根（いちのげんしるいじょうこん）という。
@ja
Em matemática, as raízes n-ési ...... lados com um vértice sobre 1.
@pt
En matemática, las raíces n-és ...... dicho plano, siempre que n>2.
@es
En mathématiques, une racine d ...... rimitive de l'unité d'ordre n.
@fr
In de wiskunde zijn voor een g ...... lhoeken met een hoekpunt op 1.
@nl
In der Algebra werden Zahlen, ...... , -te Einheitswurzeln genannt.
@de
In matematica, le radici -esim ...... o le soluzioni dell'equazione:
@it
In mathematics, a root of unit ...... e characteristic of the field.
@en
Pierwiastek z jedynki n-tego s ...... że być w szczególności ciało .
@pl
Корни n-й степени из единицы — ...... инейкой, представлениях групп.
@ru
label
1の冪根
@ja
Eenheidswortel
@nl
Einheitswurzel
@de
Pierwiastek z jedynki
@pl
Racine de l'unité
@fr
Radice dell'unità
@it
Raiz da unidade
@pt
Raíz de la unidad
@es
Root of unity
@en
Корни из единицы
@ru
