Let $z \in \mathbb{C}$ be a D1207: Complex number.
An D548: Ordered pair $(r, \theta)$ is a polar representation for $z$ if and only if

(1)	\begin{equation} r \in [0, \infty) \end{equation}
(2)	\begin{equation} \theta \in \mathbb{R} \end{equation}
(3)	\begin{equation} z = r e^{i \theta} \end{equation}