Finding the value of an integral $\int_{|z|=3}\frac{2z^2-z-2}{z-\omega}dz$ What is the value of $$\int_{|z|=3}\frac{2z^2-z-2}{z-\omega}dz$$ when $|\omega|>3$. I know that when $|\omega|<3$ the value is $2\pi i(2\omega^2-\omega-2)$.

Note that when $|\omega|>3$, the function $\displaystyle \frac{2z^2-z-2}{z-\omega}$ is holomorphic in an open set containing $\{|z|\leq3\}$. Therefore, the integral is zero by Cauchy's integral theorem.
