Zeros and Poles of complex functions
This visualization shows what happens when you have zeros and poles
in the complex function plane.
Each of the colored points either corresponds to a zero or a pole
of a rational function. The exponent of the point can be changed by the slider.
Up to four such special points can be visualized. The exponents $\alpha_i$ can eb changed
by the sliders.
Negative exponents correspont to poles positive exponents correspond to roots.
The image of this map applied to a grid of polar coordinates is shown.
Moving the slider on the bottom lets the polar grid rotate around the origin.