This example shows the identity function, i.e. f(z) = z. You can also alter the "zero" of the function, i.e. to show a function f(z) = z - a for arbitrary a.
The identity function is not enormously interesting, however, it serves as a useful reference point, to help understand the color scheme for the domain colouring, and also to understand the representation of f(z) on the subset of the domain represented by the white circle.