In the left disk, you can change by the mouse the variable z and
the white circle of animation.
The constant a can be changed in the right side disk.
In this example you are not allowed to take the a outside the disk.
1. Find a and b such that z belongs to the light blue area if and only if a < |z| < b.
2. Take z0 in the disc.
What happens with w if you put z in the place w0 = f(x0) ?
What happens with w if z describes a circle which is not centered at the origin ?