Mathematics - Complex Analysis - Complex functions - Domain Coloring

Show the complex plane colored by a complex function f(z). Each point z gets a color based on arg(f(z)) (hue) and |f(z)| (brightness). Let the student toggle between functions: f(z)=z² (doubles angles, squares distances), f(z)=1/z (inverts), f(z)=eᶻ (maps horizontal strips to wedges), f(z)=sin(z). T