Functions of Complex Variables

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch cut and other issues.

ReferenceReference

Visualization

ContourPlot, DensityPlot plot over the complex plane, potentially coloring by phase

ParametricPlot plot conformal mappings

Integration

Integrate symbolic integrals taking account of complex variables

PrincipalValue option for specifying whether to take principal values

NIntegrate numerical integration around contours in the complex plane

Residue residue at a pole

Symbolic Manipulation

ComplexExpand symbolically expand into real and imaginary parts

Reduce reduce polynomial systems over complex variables

Basic Functions »

Abs ▪ Arg ▪ Conjugate ▪ Re ▪ Im ▪ RandomComplex ▪ ExpToTrig ▪ ...

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