- 12

- 0

**1. The problem statement, all variables and given/known data**

integral |z|=1 of sinz/z

^{2}dz

**2. Relevant equations**

Rule #1 if f(z) has a simple pole at z

_{0}, then

Res[f(z),z

_{0}] = lim(as z goes to z

_{0}) (z - z

_{0})*f(z)

Rule #2 if f(z) has a double pole at z

_{0}, then

Res[f(z),z

_{0}] = lim(as z goes to z

_{0})d/dz (z - z

_{0})

^{2}*f(z)

Rule #3 If f(z) and g(z) are analytic at z

_{0}, and if g(z) has a simple zero at z

_{0}then,

Res[f(z)/g(z), z

_{0}] = f(z

_{0})/g'(z

_{0})

Rule #4 If g(z) is analytic and has a simple zero at z

_{0}then,

Res[1/g(z), z

_{0}] = 1/g'(z

_{0})

**3. The attempt at a solution**

Just confused on which one to use? Would I integrate first? And if so what would my z

_{0}be in Rest[..., z

_{0}]

Thanks