Relationship between logarithm (multivalued) and positive integer exponents
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Theorem
Let $z \in \mathbb{C}$ and $n$ be a positive integer. Then the following formula holds: $$\mathrm{Log} \left( z^n \right) \subset n \mathrm{Log}(z),$$ where $\mathrm{Log}$ denotes the logarithm (multivalued) and $n \mathrm{Log}(z)=\left\{nw \colon w \in \mathrm{Log}(z)\right\}$.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.10
