Arccosine Logarithmic Formulation

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


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

where $\arccos x$ is the arccosine and $i^2 = -1$.

Proof
Assume $ y \in \R $, $ 0 \le y \le \pi $.