# Definition:Inverse Sine/Complex/Arcsine

(Redirected from Definition: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 $1 - z^2$.