Definition:Inverse Tangent/Complex/Arctangent

Definition
The principal branch of the complex inverse tangent function is defined as:
 * $\arctan \left({z}\right) := \dfrac 1 {2 i} \operatorname{Ln} \left({\dfrac {i - z} {i + z}}\right)$

where $\operatorname{Ln}$ denotes the principal branch of the complex natural logarithm.

Also defined as
Some sources report this as:
 * $\arctan \left({z}\right) := \dfrac 1 {2 i} \operatorname{Ln} \left({\dfrac {1 + iz} {1 - iz}}\right)$

Also see

 * Derivation of Complex Arctangent from Inverse Tangent Multifunction