Logarithm (multivalued) of the exponential

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.2.2