“nth root of unity”的概念、定义、翻译、参考文献-科学参考

nth root of unity

Mathematics

A complex number z such that zⁿ = 1. The n distinct nth roots of unity are e^i2kπ‎/n(k = 0, 1,…, n−1), or

$cos \frac{2 k π}{n} + i sin \frac{2 k π}{n} (k = 0, 1, \dots, n - 1) .$

They are represented in the complex plane by points that lie on the unit circle and are vertices of a regular n-sided polygon. The nth roots of unity for n = 5 and n = 6 are shown in the figure. The nth roots of unity always include the real number 1 and also include the real number−1 if n is even. The non-real nth roots of unity form pairs of conjugates.

单词	nth root of unity
释义	nth root of unity Mathematics A complex number z such that zⁿ = 1. The n distinct nth roots of unity are e^i2kπ‎/n(k = 0, 1,…, n−1), or $cos \frac{2 k π}{n} + i sin \frac{2 k π}{n} (k = 0, 1, \dots, n - 1) .$ They are represented in the complex plane by points that lie on the unit circle and are vertices of a regular n-sided polygon. The nth roots of unity for n = 5 and n = 6 are shown in the figure. The nth roots of unity always include the real number 1 and also include the real number−1 if n is even. The non-real nth roots of unity form pairs of conjugates.
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