Complex numbers provide an important method of representation for many mayor problems in analysis and geometry. They prove to be an elegant means for solving equations in mathematics, but also for mathematizing problems in physics and technology. As vectors of the plane with a multiplicative structure, they serve to illustrate and algebraize geometric objects and operations.
This book provides a clear introduction to the arithmetic of complex numbers and deals comprehensively with their role both in solving equations and in the geometry of the plane and introduces conformal mappings and Möbius transformations. References to the historical development of central mathematical results are discussed. Exercises with solutions to the individual chapters and an appendix on calculating with complex numbers and conformal mapping in MAPLE complete the book.
This fourth edition has been expanded to include sections on mapping geometry and in-depth study of Möbius transformations and non-Euclidean geometry. The new edition also contains numerous color illustrations.