The best way to learn complex analysis is to start with a strong foundation in calculus and basic algebra. It is also helpful to have a good understanding of real analysis and linear algebra. Practice solving problems and working through proofs will also aid in understanding the subject.
A good complex analysis book should cover topics such as complex numbers, analytic functions, contour integration, series and sequences, and conformal mapping. Other important topics include the Cauchy-Riemann equations, the Cauchy integral theorem, and the residue theorem.
As mentioned before, a strong background in calculus, basic algebra, real analysis, and linear algebra is necessary for studying complex analysis. It is also helpful to have a good understanding of trigonometry and geometry.
Complex analysis has many applications in physics, engineering, and other fields. It is used in signal processing, fluid dynamics, electromagnetism, and many other areas. It can also be applied in computer graphics and image processing.
Some recommended books for beginners in complex analysis include "Complex Variables and Applications" by James Ward Brown and Ruel V. Churchill, "Visual Complex Analysis" by Tristan Needham, and "A First Course in Complex Analysis" by Matthias Beck, Gerald Marchesi, and Dennis Pixton. It is also helpful to consult with a professor or advisor for personalized recommendations.