(a) Evaluate $\oint_C \frac{(z+1)}{(z-1)(z+2)} dz$ where $C$ is the c…

Question

(a) Evaluate $\oint_C \frac{(z+1)}{(z-1)(z+2)} dz$ where $C$ is the circle $|z| = 3$, using Cauchy integral formula.

(b) Find the Taylor series expansion of $\sin z$ at $z = \frac{\pi}{3}$.

(c) Using Cauchy Residue theorem, evaluate $\oint_C \frac{(1+2z)}{(z-1)(z-2)(z+3)} dz$ where $C$ is the circle $|z| = 4$.