Play

Undertanding function action on points: Type function, move point in domain, see image in codomain
Understanding domain coloring by argument: Move point in domain, see point in codomain, color point in domain until you fill in the whole domain
Understanding pushing paths forward: Draw path in domain, see pushforward of path in codomain
Understanding the vector field approach: See vector field play with different functions

Practice

Function action on points: Given point in domain, where is it mapped in the codomain?
Finding zeros with phase diagram: Find zero of given function and check that they are zeros (I solumnly swear that I checked)
Finding purely real and imaginary points with phase diagram: Click on point in domain which is sent to positive real axis (negative, imaginary)
Winding numbers of paths with phase diagram 1: How many times does the pushforward of the given path wind around the origin in the codomain?
Winding numbers of paths with phase diagram 2: Draw a path in domain which will wind n times around the origin in the codomain.
Find zeros of functions (Vector Field): Where are zeros of function
Finding purely real and imaginary points (Vector Field): Click on point with real, imaginary value
Adding and Subtracting Complex Numbers Graphically