Suppose ( w = f(z) ) is a fractional linear map satisfying ( f(f(f(f(f(z)))))) = z ), and is not the identity. Show that such a map is not of the hyperbolic type.
a) The map ( w = {az + b}/{cz + d} ) is hyper

bolic.
b) The map ( w = {az + b}/{cz + d} ) is elliptic.
c) The map ( w = {az + b}/{cz + d} ) is parabolic.
d) The map ( w = {az + b}/{cz + d} ) is loxodromic.