Consider the Riemann surface $N$ of the algebraic function given by
$$ w= ((z-2)^2 (\sqrt(z) + i))^{\frac{1}{3}} $$
What are the branching points of S? What are their orders? What is the genus?
I think the branching points are $z=2$ and $z= 1$ with orders of $2$ and $1$ respectively? Am I correct in my assessment? Regarding the Riemann surface I know that there is a correspondence between Riemann surfaces and algebraic fuctions. Is the genus of this Riemann surface equal to 1?