Definition:Inverse Tangent/Complex/Arctangent

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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


Sources