Root of unity

One of $N$ equally spaced points on the unit circle, the exponential kernel a DFT sum is built from.

The exponential kernel $e^{-2\pi ikn/N}$ appearing in the discrete Fourier transform is a root of unity: one of the $N$ equally spaced points on the unit circle, $e^{-2\pi ik/N}$ raised to the $n$ -th power. The DFT's own orthogonality is the discrete analogue of continuous sine/cosine orthogonality, with a finite sum over roots of unity standing in for an integral.

Examples

The four 4th roots of unity are $1, i, -1, -i$ , equally spaced around the unit circle.