I am studying complex analysis. And I am using J. Bak and D.J. Newman's book.(springer) And now my studying topic is conformal map. In addition to this book, I want to learn other book names which explains this topic more clearly and suggested book's content should be parallel to that of my using book. And this book sould contain more examples as well. Thank you for your suggestions:)
I have found this book: Flanigan "Complex Variables" to be excellent, especially if you are studying on your own. I also am self-taught and love this book.
I am not sure how advanced you are and how confident you feel about what you have studied. However, beginning with Chapter 3, you can get excellent, clear, detailed explanations of the material. Additionally, what I especially like about this book is that it has many pictures so you can really see what is going on.
In that it is the Dover edition of a classic, it is not expensive - especially compared to the outrageous prices of other books.