I'm reading Conway's complex analysis book and on page 107 he proved the following theorem:
I didn't understand this part of the proof:
Why $f(z)=\frac{1}{2\pi i}\int_{\gamma} \frac{f(w)}{w-z}dw$?
What the winding numbers $n(\gamma_2,z)$ and $n(\gamma_1,z)$ have to do with everything?
Best Answer
On page 92 he stated the following theorem:
Now it suffices to use this corollary to have the hypothesis of this theorem on page 84: