Definition:Inverse Cotangent/Complex/Definition 2

Definition
Let $z \in \C$ be a complex number.

The inverse cotangent of $z$ is the multifunction defined as:
 * $\cot^{-1} \left({z}\right) := \dfrac 1 {2 i} \ln \left({\dfrac {z + i} {z - i}}\right) + 2 k \pi$

where:
 * $\ln$ denotes the natural logarithm (as a multifunction).

Also see

 * Equivalence of Definitions of Complex Inverse Cotangent Function


 * Definition:Complex Arccotangent