Advice for choosing a book in Complex Analysis.

Question

I am a 4th year mathematics undergraduate student. I took a "Complex Variables" (complex analysis made less rigorous) course in second year, though I feel at the time I wasn't able to properly appreciate the subject since I was in second year. Now, I am in 4th year and I have a background in real analysis, including two introductory course in the subject, a course in measure theory, a course in topology, and (currently) a course in functional analysis. I am looking for a complex analysis book that I will enjoy in my spare time.

What I am looking for:

1. Most importantly, lots of exercises that have (at least some) selected solutions
2. A book that explains well and emphasizes the theory

Something under $200 for a physical copy would be nice (though beggers can't be choosers).

Thanks in advance for the advice!

Answer 1

Visual Complex Analysis by Tristan Needham is often recommended. It is a first course on complex analysis. Here is a preview.

Answer 2

Serge Lang wrote a book called Complex Analysis (Springer GTM 103) that has an accompanying solutions manual by Rami Shakarchi somewhere. According to an Amazon review it has a topological flavor, which might be appreciated since you have prior experience with topology.

Note: I have not read the book.

Answer 3

Try the book "Introduction to Complex Analysis" here: https://mtaylor.web.unc.edu/notes/complex-analysis-course/. I've read it, and I think it is good.

Answer 4

Look at this page and download "basic complex analysis" and "selected topics in complex analysis". They are really good notes.