I have just started taking complex analysis course,The following problem is given in my class.Please help me solving it. Thnx in advance.
Suppose $f(z)$ is analytic and satisfies the relation $|f(z)-1| < 1 $ in a region $\Omega$ Show that $\displaystyle \int_\gamma \frac{f'(z)}{f(z)}=0$ for every closed curve $\gamma$ in $\Omega$
I am only taught upto Cauchy's Theorem which I think is applicable for disc. Now here nothing is mentioned about $\Omega$, only thing I know that it is open connected.So how can I apply Cauchy's Theorem here?
Being very new to complex analysis I appologise if I am missing something very simple or doing something very much wrong.
Please help me to solve this question. Thnx again.