Am revising Complex Analysis, and have come across this equality:
For $R\gt 1$ and $|a|\lt 1$ $$\frac{1}{2\pi i}\int_{\gamma (0;1)}\frac{\overline{f(z)}}{z-a} dz = \overline{\frac{1}{2\pi i}\int_{\gamma (0;1)}\frac{{f(z)}}{z(1-\overline{a}z)} dz}$$
And this supposedly follows from the Cauchy Integral Formula, that $$f(w)=\frac{1}{2\pi i}\int_{\gamma (w;r)}\frac{f(z)}{z-w}dz$$
But I just can't see how to apply this to get the desired result?
If someone could explain it to me, that would be really appreciated. Thanks.