3D Plots of Rational Functions of a Complex Variable

This Demonstration shows a complex rational function as a 3D plot of , in which colors depend on the quadrant in which falls. A rational function is the quotient of two polynomials, and . This Demonstration uses polynomials of the form and , where the coefficients and are complex numbers. Suppose that and have no common roots. Then the zeros of are the zeros of , while the zeros of are the poles of , which show as tubes rising to infinity.