$$\int_C \operatorname{Log}\left(1-\frac 1 z \right)\,dz$$ where $C$ is the circle $|z|=2$
I don't even know how you would begin doing this.
I understand $\operatorname{Log}(z)=\ln|z|+i\arg(z)$, but I don't think it helps in this case.
2026-04-11 12:34:39.1775910879
Complex analysis integration with logs
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Hint: $\operatorname {Log} (1-w) = -(w+w^2/2 +w^3/3 + \cdots )$ for $|w|<1.$