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:
 * $\cot^{-1} \left({z}\right) := \left\{{\dfrac 1 {2 i} \ln \left({\dfrac {z + i} {z - i}}\right) + k \pi: k \in \Z}\right\}$

where $\ln$ denotes the complex natural logarithm as a multifunction.

Also see

 * Equivalence of Definitions of Complex Inverse Cotangent Function


 * Definition:Inverse Hyperbolic Cotangent/Complex/Definition 2


 * Definition:Complex Arccotangent