# Definition:Inverse Hyperbolic Cosine/Complex/Principal Branch

## Definition

The principal branch of the complex inverse hyperbolic cosine function is defined as:

$\forall z \in \C: \map \Arcosh z := \map \Ln {z + \sqrt {z^2 - 1} }$

where:

$\Ln$ denotes the principal branch of the complex natural logarithm
$\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.