# Definition:Inverse Cosine/Complex/Arccosine

## Definition

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

$\map \arccos z = \dfrac 1 i \, \map \Ln {z + \sqrt {z^2 - 1} }$

where:

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