Logarithm (multivalued) of the exponential

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Theorem

The following formula holds: $$\mathrm{Log}\left( \exp(z) \right) = \{ z +2k\pi i \colon k \in \mathbb{Z}\},$$ where $\mathrm{Log}$ denotes the logarithm (multivalued), $\exp$ denotes the exponential, $\pi$ denotes pi, and $i$ denotes the imaginary number.

Proof

References