Visualizing Complex Functions

The reason it is easier is because when you multiply two complex numbers, the result’s magnitude is the product of the two original magnitudes, and the result’s angle is the sum of the the two original angles. Similarly to the square, this function triples the number of hues around the pole and triples the density of the contours. Opposing poles appear out of thin air along the imaginary axis and pull back, leaving a sequence of vertical contours on the negative real side of the function in similar manner to .

Source: vankessel.io