I am a physics undergrad with no formal background in complex analysis. I have done complex analysis at the level of the first 4 chapters (till Complex integration) from Churchill and Brown. I am very keen to explore algebraic geometry, and I am thinking of starting with Rick Miranda's book on Algebraic Curves and Riemann Surfaces.
What are the complex analysis prerequisites for atleast starting this book (first 2-3 chapters)? Would first 4 chapters of Churchill and Brown be enough. If not, then what and from where should I study?
Also what are the topology prerequisite? I have done the 2nd chapter of Munkres? Is that enough?