### Complex Logarithm (Principle Value) For some [[Complex Numbers|Complex Number]] $z\in \C$ expressed in [[Polar Coordinates]] $re^{i\theta}$, the [[Principle Value]] $\op{Log} z$ is equal to the sum of the [[Logarithms|Logarithm]] of the [[Absolute Value]] of $z$ and $i$ times the [[Argument]] of $z$. $\huge \forall z \in \C : \op{Log}(z) = \ln re^{i\theta} = \ln |z| + i \arg z $