The expressions in Equation ??? are called the polar forms of N, the name being chosen to suggest that the representation of N by H and U is analogous to the representation of a complex num...The expressions in Equation ??? are called the polar forms of N, the name being chosen to suggest that the representation of N by H and U is analogous to the representation of a complex number z by a positive number r and a phase factor:
To visualize Möbius transformations it is helpful to focus on fixed points and, in the case of two fixed points, on two families of clines with respect to these points.