Definition:Inverse Cotangent/Complex/Definition 2

Definition
Let $S$ be the subset of the complex plane:
 * $S = \C \setminus \left\{{0 + i, 0 - i}\right\}$

The inverse cotangent is a multifunction defined on $S$ as:


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

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