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
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $7$