Rational Functions with Complex Coefficients

A quotient of two polynomials and , , is called a rational function. This Demonstration plots rational functions using 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 , and the zeros of are the poles of . Zeros are shown in white in centers of black patches, and poles are shown as red points.

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