Book for complex analysis covering specific requirements

Question

I want a book on Complex Analysis for self-study which covers the following syllabus in detail.

• Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions.

• Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem.

• Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.

I searched for various books here which mostly included

• Functions of one complex variable by J.B.Conway.
• Visual complex analysis-Needham
• Stein Shakarchi.

The two of them Conway and Stein don't contain examples and exercises for self -study.

Needham is too broad to be used as a text.

I want to get a book which will cover the syllabus in detail and give handsome exercises and examples and hints to the exercises(if possible).

Please suggest a text accordingly as it is not possible for me to find atext on my own.

Answer 1

My favorite: L. V. Ahlfors: Complex Analysis. Also includes many examples and exercises.

Answer 2

My favorite:

Robert B. Burckel: An introduction to classical complex analysis, Vol.1 (Birkhäuser).

Answer 3

A first course in complex analysis with application by Dennis G.Zill. this book covers all topics that you mentioned above.

Answer 4

Complex Analysis-Bak, Neumann should suit you.