Chapter 14.11, Problem 14MP

In Problems 13 and 14, find the residues at the given points.

$\begin{array}{lllll}\hfill & \text{ (a) }\hfill & \frac{\ln (1+2z)}{z^2}\hfill & \text{ at }\hfill & 0\hfill \end{array}$

(b) $\frac{1}{z}\sin (2z+5)$ at $\infty$

(c) $\frac{z^3}{4z^4+1}$ at $\frac{1}{2}(1+i)$

(d) $\frac{z\sin 2z}{{(z+\pi )}^2}$ at $-\pi$