Definition:Inverse Tangent/Complex/Arctangent

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

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

Also defined as
Some sources report this as:
 * $\map \arctan z := \dfrac 1 {2 i} \, \map \Ln {\dfrac {1 + i z} {1 - i z} }$

Also see

 * Derivation of Complex Arctangent from Inverse Tangent Multifunction