Definition:Exponential Function/Complex/Limit of Sequence

Definition

Let $\exp: \C \to \C \setminus \set 0$ denote the (complex) exponential function.

The exponential function can be defined as a limit of a sequence:

$\ds \exp z := \lim_{n \mathop \to \infty} \paren {1 + \dfrac z n}^n$

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

Also see

• Equivalence of Definitions of Complex Exponential Function

• Results about the exponential function can be found here.