Definition:Inverse Sine/Complex/Definition 1

Definition
Let $z \in \C$ be a complex number.

The inverse sine of $z$ is the multifunction defined as:
 * $\sin^{-1} \left({z}\right) := \left\{{w \in \C: \sin \left({w}\right) = z}\right\}$

where $\sin \left({w}\right)$ is the sine of $w$.

Also see

 * Equivalence of Definitions of Complex Inverse Sine Function


 * Definition:Complex Arcsine