# Definition:Inverse Cosine/Complex/Definition 1

Let $z \in \C$ be a complex number.
The inverse cosine of $z$ is the multifunction defined as:
$\cos^{-1} \left({z}\right) := \left\{{w \in \C: \cos \left({w}\right) = z}\right\}$
where $\cos \left({w}\right)$ is the cosine of $w$.