I've read the notes and tried to find similar sample problems, but I just cant get my head around this stuff . If somebody could work through this one question it would be much much appreciated:

Let $\displaystyle \gamma_1$ denote the circle $\displaystyle |z|=4 \,$ , and $\displaystyle \gamma_2$ the boundary of the square with sides along $\displaystyle x = \pm 1$ and $\displaystyle y= \pm 1$, both oriented clockwise. Use Cauchy-Goursat and its consequences to show that:

$\displaystyle \int_{\gamma_1} f(z) \, dz \, = \int_{\gamma_2} f(z) \, dz \,$

when

$\displaystyle f(z)=\frac{1}{3z^2+1}$