A unit circle is any circle whose radius is $1$, and is used and a base simplification for any circle. Using [[Coordinate System|coordinates]] of the [[Cartesion Plane]] whose origin is the center of this unit circle, the set of all points in that circle are equal to: $\huge \begin{align} C_{1} &= \setbuild{ (x,y) \in \R \times \R }{x^{2}+y^{2}=1}\\ \end{align}$ When talking about unit circle in the [[Complex Plane]], we denote the [[Set]] of all points as: $\huge \begin{align} S^{1} &= \left\{ {z\in \C}: { |z| =1} \right\} \end{align} $