Definition 31.5.1 (Branch of Logarithm).label Let $U \subset \complex$ be a connected open set with $0 \not\in U$ and $f \in C(U; \complex)$, then $f$ is a branch of the logarithm if for every $z \in U$, $z = \exp(f(z))$.
Definition 31.5.1 (Branch of Logarithm).label Let $U \subset \complex$ be a connected open set with $0 \not\in U$ and $f \in C(U; \complex)$, then $f$ is a branch of the logarithm if for every $z \in U$, $z = \exp(f(z))$.
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