I'm having a lot of trouble understanding how to approach these kinds of problems, if anyone could explain the approach, it would be really helpful. The problem is as follows:
The function $f(z)$ is given by
$$f(z)=(z+1)^{\frac{1}{2}}\ln{\left(z-\sqrt{3}\right)}$$
The branch of this function is chosen such that
$$-\frac{3\pi}{2}<\arg{(z+1)}\leq \frac{\pi}{2} \\ -\frac{2\pi}{3}<\arg{\left(z-\sqrt{3}\right)}\leq \frac{4\pi}{3}$$
Draw a clearly labelled diagram showing the branch cuts and the polar coordinates used to evaluate the function.