Definition:Exponential Function/Complex/Power Series Expansion

Definition
Let $\exp: \C \to \C \setminus \left\{ {0}\right\}$ denote the (complex) exponential function. The exponential function can be defined as a (complex) power series:

The complex number $\exp z$ is called the exponential of $z$.

Also see

 * Equivalence of Definitions of Complex Exponential Function