Identify Zeros and Singularities
Complex plots allow you to identify features such as zeros, poles and other singularities, based on patterns that the colors make.
Around a zero, ComplexPlot goes through blue, red, yellow and green in a counterclockwise direction.
Around a pole, the colors are in a clockwise direction.
Around a repeated pole or zero, the colors cycle multiple times. The following plot indicates a zero of order 3.
At an essential singularity, the plot shows infinite cycling through the colors.