# Domain Coloring for Common Functions in Complex Analysis

Domain Coloring for Common Functions in Complex Analysis

A domain coloring or phase portrait is a popular and attractive way to visualize functions of a complex variable. The absolute value (modulus) of the function at a point is represented by brightness (dark for small modulus, light for large modulus), while the argument (phase) is represented by hue (red for positive real values, yellow-green for positive imaginary values, etc.). This Demonstration creates domain colorings for many well-known functions in complex analysis: trigonometric and exponential functions, Möbius transformations, the Joukowski map, the Koebe function, Weierstrass functions, gamma and beta functions, and the Riemann zeta function.

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