Discussion
How many values does \( \log z \) take for a given non-zero \( z \)?
Answer: B
Writing \( z = re^{i\theta} \),
\[ \log z \;=\; \ln r + i(\theta + 2n\pi), \qquad n \in \mathbb{Z}, \]
so every choice of \( n \) gives a value. Restricting \( \theta \) to a range of width \( 2\pi \) picks the principal value, and the branch cut is where that restriction is imposed
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