## Quick Reference

A complex number *z* such that *z*^{n}=1. The *n* distinct *n*-th roots of unity are *e*^{i2kπ/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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