Definition:Inverse Sine/Complex/Arcsine

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

where:
 * $\Ln$ 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