Stereographic Projection Animation.

In the complex plane, where is z=infinity located? There is this multivaluedness in the complex plane. No matter in which direction you approach r=infinty, you'll always reach z=infinty.
So to create the one-by-one relation, where every point is associated with only a single point, we use stereographic projection in which every point of the complex plane is associated with a point on the sphere. z=infinity point corresponds to only one point on the sphere, and that is (0, 0, 2) point i.e the North Pole point on the sphere.
ENJOY and believe in the supremacy of Mathematics.

[jakfrost]

which software are you using for graphics