Overview

n-th root of unity


Show Summary Details

Quick Reference

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.


Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.