Definition:Natural Logarithm/Complex/Definition 2

Definition
Let $z \in \C_{\ne 0}$ be a non-zero complex number.

The complex natural logarithm of $z$ is the multifunction defined as:


 * $\ln \paren z := \set {w \in \C: e^w = z}$

Also see

 * Equivalence of Definitions of Complex Natural Logarithm