04
Here we see another visualization of the rational function shown on the previous page. The colored density plot has been supplemented by a few contour lines. Along these lines the absolute value of the function is constant. For this image, the constant values are 0.05 (the largest 'circle'), 0.1, 0.2, 0.4, 0.8, and 1.6.
The positions of the poles are given by the zeros of the denominator. These zeros are the third unit roots. The colors near the origin are between blue and green (cyan) indicating values near the negative real axis. Indeed, the function value at z=0 is -1.