I have a question that I cannot wrap my head around. How would I compute this integral using complex analysis techniques?
$$ \int_{\gamma(0;1)} \frac{\text{Im}(z)}{z-\frac{1}{2}} \,dz $$
I was thinking about whether I need to consider another function which is holomorphic (because $\text{Im}(z)$ isn't - correct me if I'm wrong). For example, perhaps I need to consider a function like $f(z) = z$, which would be holomorphic along $\gamma$ (again correct me if I am wrong).
How would I go about solving this problem?