Logarithm of exponential

Theorem

The following formula holds for $-\pi < \mathrm{Im}(z) \leq \pi$: $$\log(\exp(z))=z,$$ where $\log$ denotes the logarithm and $\exp$ denotes the exponential.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 3.3.4