The mapping w = 1/z is called the reciprocal transformation and maps the z; plane one-to-one and onto the w; plane except for the point z = 0;, which has no image, and the point w = 0;, which has no preimage or inverse image. Using exponential notation w = rho*exp(i*phi);, we see that if z; = r*exp(i*theta) <> 0;, then we have w; = rho*exp(i*phi) = 1/z = 1/r; exp(i*theta);. It is convenient to extend the system of complex numbers by joining to it an "ideal" point denoted by infinity; and called the point at infinity. This new set is called the extended complex plane. The reciprocal transformation maps the "extended complex z-plane" one-to-one and onto the "extended complex w-plane"