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 .