Complex inverse sine
= Complex inverse sine
{title2=$\arcsin z$}
The principal complex inverse sine on
$$
\mathbb C\setminus\bigl((-\infty,-1]\cup[1,\infty)\bigr)
$$
is the branch
$$
\arcsin z=\int_0^z\frac{dt}{\sqrt{1-t^2}}
$$
whose derivative equals one at zero.
It is the complex sine member of the <inverse trigonometric functions>.