Definition:Inverse Cotangent/Complex/Definition 1
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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:
- $\forall z \in S: \cot^{-1} \left({z}\right) := \left\{{w \in \C: \cot \left({w}\right) = z}\right\}$
where $\cot \left({w}\right)$ is the cotangent of $w$.