I will be doing a reading course in the complex analysis starting on this Fall Semester. The assigned book is Rudin's Real and Complex Analysis. From my understanding, Rudin treats complex analysis very elegantly, but very terse. I am curious if you could suggest some books in the complex analysis that can accomodate Rudin, with particular emphasis on the extensive treatment and/or clear explanations. I am embarrassed to ask my professor as I do not want to impose a bad impression on me.
Also, are previous chapters in Rudin-RCA a must requirement for later chapters in the complex analysis? I am currently reading through Berberian and Kolmogorov/Fomin to learn some basics of measure theory and banach space, but I have not completely learned them yet.