Arcsine Logarithmic Formulation

Theorem
For any real number $x$ s.t. $-1 \le x \le 1$,


 * $ \displaystyle \arcsin x = -i \ln \left({ \sqrt{1-x^2} + ix }\right) $

where $\arcsin x$ is the arcsine and $i^2 = -1$.

Proof
Assume $ y \in \R $, $ -\frac \pi 2 \le y \le \frac \pi 2 $.