Arctangent Logarithmic Formulation

Theorem
For any real number $x$:


 * $\arctan x = \dfrac 1 2 i \ln \left({\dfrac{1 - i x} {1 + i x}}\right)$

where $\arctan x$ is the arctangent and $i^2 = -1$.

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

Also see

 * Arcsine Logarithmic Formulation
 * Arccosine Logarithmic Formulation
 * Arccotangent Logarithmic Formulation
 * Arcsecant Logarithmic Formulation
 * Arccosecant Logarithmic Formulation