Wolfram Language

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.

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