单位根 Root of unity

（重定向自Roots of unity）

Las 5 soluciones de la raíz quinta de la unidad en el plano complejo

Plot of z3 − 1, in which a zero is represented by the color black.

Plot of z5 − 1, in which a zero is represented by the color black.

数学上， $n \,$ 次单位根是 $n\,$ 次幂为1的复数。它们位于复平面的单位圆上，构成正n边形的顶点，其中一个顶点是1。

z^n = 1 \qquad (n = 1, 2, 3, \cdots )

这方程的复数根 $z \,$ 为 $n \,$ 次单位根。

单位的 $n \,$ 次根有 $n \,$ 个：

e^{\frac{2 \pi k {\mathrm{i}} }{n} } \qquad (k = 0, 1, 2, \cdots, n - 1)

。

单词	Roots of unity
释义	Roots of unity 中文百科单位根 Root of unity （重定向自Roots of unity）数学上， $n \,$ 次单位根是 $n\,$ 次幂为1的复数。它们位于复平面的单位圆上，构成正n边形的顶点，其中一个顶点是1。 $z^n = 1 \qquad (n = 1, 2, 3, \cdots )$ 这方程的复数根 $z \,$ 为 $n \,$ 次单位根。单位的 $n \,$ 次根有 $n \,$ 个： $e^{\frac{2 \pi k {\mathrm{i}} }{n} } \qquad (k = 0, 1, 2, \cdots, n - 1)$ 。英语百科 Root of unity 单位根（重定向自Roots 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.
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Roots of unity

单位根 Root of unity

Root of unity 单位根