Evaluating Integrals: Need Help Factorising Denominator

[Fixxxer125]

Homework Statement

Evaluate the integral

Homework Equations

I can substitute

and thus end up with

The Attempt at a Solution

I then expand the denominator out and end up with 1/

However I then assume I need to factorise the top line of that fraction as this will be the denominator in my integral, so I want to factorise this and find where it equals zero and thus where the poles are. However I'm unsure how to do this and need help! Thanks

 

[clamtrox]

Just multiply upstairs and downstairs by z, carry z^2 in downstair inside the brackets, and solve the 2nd order equation.

 

[Fixxxer125]

sorry I don't really understand what you are saying!

 

[clamtrox]

$$I = -i \oint_{|z|=1} \frac{dz}{z(5-3(\frac{z-z^{-1}}{2i}))^2} = -i \oint_{|z|=1} \frac{ z dz}{\left[5z-3(\frac{z^2-1}{2i})\right]^2}$$
and then solve
$$5z-3(\frac{z^2-1}{2i}) = 0$$
(and remember how many of each pole there are!)

 

[Fixxxer125]

thanks! I'll give it a go