# Complex analysis

1. Nov 24, 2005

### fahd

hi there
im confused with this question..
Integrate 1) Sin(1/z) dz
and 2) Z sin (1/Z^3)

where Z is any complex number., over C which is a circle of radius 1 centred at 0

2. Nov 25, 2005

### matt grime

Where are the poles and what are its residues at each pole?

3. Nov 25, 2005

### benorin

Use Laurent series

4. Nov 27, 2005

### HallsofIvy

Presumably, you know the Taylor's series for sin(z). Replace z in that series by 1/z and 1/z3 to get the Laurent Series for sin(1/z) and sin(1/z3) respectively. Then the integrals should be easy.