A homeomorphism f is said to be quasiconformal, with given complex dilatation μ, in a domain G of the complex plane, if it satisfies the Beltrami equation fz, = μfz, (1) where μ =μ(z) is a complex-valued measurable function on G with μ< k< 1, and fz=1/2(fx-ify), fz = 1/2(fx + ify). (2) There are two principal problems: finding such quasiconformal homeomorphisms of the whole plane on itself, and of the unit disk D on itself. In both cases it is well known that a homeomorphism exists and, with appropriate normalization, it is unique.