These are the 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:

The th roots of unity are so frequently used that they are often
given a special notation in the signal processing literature:

where denotes a primitive th root of
unity.^{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