A sandbox for a single complex number z. Drag the red dot (or edit the fields) and watch its Cartesian form z = x + iy and polar form z = r·eiθ stay in sync. The buttons apply basic operations so you can see them geometrically.
A modern JavaScript + Canvas port of a 1998 Java applet by Terence Tao
(originally PlaneApp.java / Plane.java).