Complex analysis textbook advise

Question

During this summer break, I want to use my time to broaden my knowledge of mathematics. I am a very motivated high school student searching for some challenging material to learn, and the two subjects I had in mind are complex analysis and probability theory.

For probability theory I already choose a book, but I am struggling a bit with finding the right complex analysis textbook. I already found two textbooks which seem pretty good to me: A Friendly Approach to Complex Analysis by Sara Maad Sasane and Complex Analysis: A First Course with Applications by Zill.

As to requirements for the book:

• The textbook must not be too broad, since I only have 6 weeks to study intensively (yes, I know it's a challenge to study most of complex analysis in 6 weeks).
• The textbook must not require a lot of prerequisities other than knowledge of single variable calculus (not a course in proof writing) and must not be too rigourous (some pictures and intuitive explanations can come in handy).

I hope someone could give some advise as to if the books I found suit my needs, if someone has experience with those books or if someone knows a book other than the two I found which suit my needs better.

Thanks in advance.

Answer 1

I would give serious consideration to Needham's book:

Visual Complex Analysis

It does not demand a huge amount by way of pre-requisites, and gives a great deal of insight into what is really important in the study of complex analysis.

Answer 2

I would recommend "Complex Variables and Applications" by Brown and Churchill.

The authors have been dead for a long time and the content of the book hasn't changed in recent new editions so you can pick up an old edition real cheap.

Answer 3

I recommend "Complex Analysis" by Lars Ahlfors or "Functions of One Complex Variable" by John B. Conway.