n-th root of unity

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A complex number z such that zn=1. The n distinct n-th roots of unity are ei2kπ/n(k=0, 1,…, n−1), or

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 n-th roots of unity for n=5 and n=6 are shown in the figure. The n-th roots of unity always include the real number 1, and also include the real number −1 if n is even. The non-real n-th roots of unity form pairs of conjugates. See also cube root of unity and fourth root of unity.

Subjects: Mathematics.

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