Mathematica has fundamental support for both explicit complex numbers and symbolic complex variables. All applicable mathematical functions support arbitrary-precision evaluation for complex values of all parameters, and symbolic operations automatically treat complex variables with full generality.
x+Iy — the complex number
I (
) —
(entered as
Esc ii Esc "imaginary
", or
Esc jj Esc)
Complex — convert a pair of reals to a complex number
Arg — argument (phase angle in radians)
Sign — normalized direction (
)
Conjugate — complex conjugate
(also entered with superscript
Esc co Esc)
ConjugateTranspose — Hermitian conjugate of a matrix (also entered with
Esc ct Esc)
ComplexExpand — expand symbolic expressions into real and imaginary parts
PowerExpand — expand symbolic expressions ignoring branch cuts
ExpToTrig,
TrigToExp — convert between complex exponentials and trig functions
GaussianIntegers — option for polynomial and number theory functions
Reduce — reduce equations and inequalities over complex numbers
RandomComplex — random complex number
