I have no idea where should I start. I have only learned line integration, Cauchy's Integral theorem and formula.
Please give me some hints on where should I begin. Do note that I have not learned very detail in this topic.
Hello,
Since $\displaystyle w\in\mathbb{C}\backslash\mathcal{C}$, the function $\displaystyle f(z)=\frac{\sin(z)}{(z-w)^2}$ has no singularity within $\displaystyle \mathcal{C}$
Hence it's a holomorphic function in $\displaystyle \mathcal{C}$ and we can apply Cauchy's integral theorem...
Cauchy's integral formula wouldn't work because w is not within $\displaystyle \mathcal{C}$