Definition:Inverse Sine/Complex/Arcsine

Definition
The principal branch of the complex inverse sine function is defined as:
 * $\arcsin \left({z}\right) = \dfrac 1 i \operatorname{Ln} \left({i z + \sqrt{1 - z^2} }\right)$

where:
 * $\operatorname{Ln}$ denotes the principal branch of the complex natural logarithm
 * $\sqrt{1 - z^2}$ denotes the principal square root of $1 - z^2$.

Also see

 * Derivation of Complex Arcsine from Inverse Sine Multifunction