## Roots of Unity

Since for every integer , we can write*th roots of unity*. The special case is called a

*primitive th root of unity*, since integer powers of it give all of the others:

^{3.7}We may also call a

*generator*of the mathematical

*group*consisting of the th roots of unity and their products. We will learn later that the th roots of unity are used to generate all the sinusoids used by the length- DFT and its inverse. The th complex sinusoid used in a DFT of length is given by

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