# Definition:Inverse Cotangent/Complex/Arccotangent

## Definition

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

$\map \arccot z := \dfrac 1 {2 i} \, \map \Ln {\dfrac {z + i} {z - i} }$

where $\Ln$ denotes the principal branch of the complex natural logarithm.

## Also denoted as

The symbol used to denote the arccotangent function is variously seen as:

• $\arccot$
• $\operatorname {acot}$
• $\operatorname {actn}$