How do I show that the following formula holds true in general:
$$\int_\phi \overline{g(z) dz} = -\int_\phi \frac{\overline{g(z)}}{z^2}dz $$
where $$\phi = e^{(2\pi i t)}, t \in [0,1]$$
If I plug $$\phi(t)$$ in and play around with the expression I get to this point:
$$-\int_{0}^1\frac{\overline{g(\phi(t))}}{e^{(2\pi it)}}2\pi i *dt $$
but I don't see how to get the $z^2$ in to the expression and how to get rid off the $2i\pi$.
Thanks for any advice!