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 power series:


 * $\exp z := \displaystyle \sum_{n \mathop = 0}^\infty \frac {z^n} {n!}$

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