This book introduces the basic concepts of complex analysis. It details how properties of a function are reflected in and can be recovered from its phase portrait. The book features color illustrations which reveal the beauty of complex functions.

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Elias Wegert is a Professor of Mathematics at the Technische Universit�t Bergakademie Freiberg. His main research interests are in Complex and Nonlinear Analysis; he is the author of a book on nonlinear Riemann-Hilbert problems and their applications. Wegert has experience in mathematical teaching at different levels for about 30 years. He is also committed to mathematical competitions for high school students.

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