This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
 Complex Numbers 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 x+ y I () — (entered as Esc ii Esc "imaginary i", or Esc jj Esc) Complex — convert a pair of reals to a complex number      Re — real part Im — imaginary part Abs — absolute value Arg — argument (phase angle in radians) Sign — normalized direction (z/z) Conjugate — complex conjugate z* (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 TUTORIALS Complex Numbers Expressions Involving Complex Variables MORE ABOUT Functions of Complex Variables Quaternions Package Algebraic Numbers RELATED LINKS Demonstrations related to Complex Numbers (The Wolfram Demonstrations Project)