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