Math Help - one last question.

1. one last question.

I just can't figure this one out (at all). ANY help would be appreciated:

Let C be the circle of centre 0 and radius 10, oriented counterclockwise. For the function $f(z)=\frac{sin(z)}{z(z-3i)(z-30i)}$ , find $\int_C f(z) \,dz$ .

2. Originally Posted by MathSucker
I just can't figure this one out (at all).f ANY help would be appreciated:

Let C be the circle of centre 0 and radius 10, oriented counterclockwise. For the function $f(z)=\frac{sin(z)}{z(z-3i)(z-30i)}$ , find $\int_C f(z) \,dz$ .
Use the residue theorem.

Note that both poles are simple!

$\int_Cf(z)dz=2\pi i \sum res(f)=2\pi i\left( \frac{\sin(0)}{(-3i)(-30i)}+\frac{\sin(3i)}{(3i)(3i-30i)}\right)=...$