Functions of Complex Variables
The Wolfram Language 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.
Complex Function Visualization »
ComplexPlot — use color to plot the phase and magnitude of a function
ComplexPlot3D — use color and height to plot the phase and magnitude of a function
ReImPlot ▪ AbsArgPlot ▪ ...
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
ResidueSum — sum the residues of a function over a region
FunctionPoles — find the poles of a meromorphic function
ComplexExpand — symbolically expand into real and imaginary parts
Reduce — reduce polynomial systems over complex variables
Basic Functions »
Abs ▪ Arg ▪ Conjugate ▪ Re ▪ Im ▪ ReIm ▪ RandomComplex ▪ ExpToTrig ▪ ...