### Nth Roots of Unity

As introduced in §3.12, the complex numbers

are called the th roots of unity because each of them satisfies

In particular, is called a primitive th root of unity.6.2

The th roots of unity are plotted in the complex plane in Fig.6.1 for . It is easy to find them graphically by dividing the unit circle into equal parts using points, with one point anchored at , as indicated in Fig.6.1. When is even, there will be a point at (corresponding to a sinusoid with frequency at exactly half the sampling rate), while if is odd, there is no point at .

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