4 . Mobius transformations of the form where is a positive real constant are called                    magnifications . The distance between any two points is magnified by the factor under this                    transformation.

              5 . Mobius transformations of the form where is a non-zero complex constant are called                    dilations . The distance of every point from the origin is magnified by the factor and the point is                    rotated about the orgin through the angle under this transformation.

              6 . Mobius transformations of the form where are called affine transformations . The                    affine transformation can be considered as the composition of a rotation, a magnification and a                    translation.

              7 . The Mobius transformation is called an inversion.

A Mobius transformation is a one-to-one function. To see this, suppose that Then