Polar Coordinates to evaluate integrals

1. Mar 28, 2012

Fixxxer125

1. The problem statement, all variables and given/known data
Use Polar coordinates to evaluate were C denotes the unit circle about a fixed point Z0 in the complex plane

3. The attempt at a solution
I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the residue theorum to evaluate the integral so I am not really sure where to go with this question? Any help would be greatly appreciated!

2. Mar 28, 2012

HallsofIvy

Staff Emeritus
Let $z= z_0+ e^{i\theta}$.

3. Mar 28, 2012

Fixxxer125

Have I done it correctly if I end up with a final answer of
2∏i(aZ02 + bZ0 + c)
Thanks!

4. Mar 28, 2012

HallsofIvy

Staff Emeritus
Yes, in fact there is the "Cauchy integral formula" that says
$$\oint \frac{f(z)}{z-z_0} dz= 2\pi if(z_0)$$

Perhaps this problem was intended as an introduction to that.

5. Mar 28, 2012

Fixxxer125

Ah yes we have done that previously, I think I just need to do practise questions to bring all the theory together. Cheers