Editing Nth root (section)

===Roots of unity===
{{Main article|Root of unity}}
[[File:3rd roots of unity.svg|thumb|right|The three 3rd roots of 1]]

The number 1 has ''n'' different ''n''th roots in the complex plane, namely

<math display="block">1,\;\omega,\;\omega^2,\;\ldots,\;\omega^{n-1},</math>

where

<math display="block">\omega = e^\frac{2\pi i}{n} = \cos\left(\frac{2\pi}{n}\right) + i\sin\left(\frac{2\pi}{n}\right).</math>

These roots are evenly spaced around the [[unit circle]] in the complex plane, at angles which are multiples of <math>2\pi/n</math>.  For example, the square roots of unity are 1 and −1, and the fourth roots of unity are 1, <math>i</math>, −1, and <math>-i</math>.