The set of all points at unit distance from the origin. In the complex plane, this is {`z`: |`z`| = 1}. Astute geometricians will realise that this is indeed the locus of points equidistant from a focus, a set vulgarly referred to as a "circle".

The *unit circle* is the boundary of the unit disk (of which, however, it is not a part). It is often used to formulate theorems of complex analysis, due to its utmost symmetry (it is, after all, a *circle*) and its uniticity.