Arcsine Logarithmic Formulation

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


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

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

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