See how a complex function w = f(z) distorts the plane. Draw a curve with the mouse in the left panel (the domain) and its image under f appears on the right. Move the cursor to preview a point z and its image f(z).
A modern JavaScript + Canvas port of a Java applet by Terence Tao (1998–2000,
originally ComplexMap.java / ComplexGrid.java).
Draw in the left panel to see the image on the right.