This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Complex

 Complexis the head used for complex numbers.
• You can enter a complex number in the form x+Iy.
• can be used to stand for a complex number in a pattern.
• You have to use Re and Im to extract parts of Complex numbers.
Enter a complex number:
Complex is the Head for complex numbers:
Enter a complex number:
 Out[1]=
Complex is the Head for complex numbers:
 Out[2]=
 Scope   (9)
Enter a purely imaginary number:
Even though there is no real part it has Head Complex:
The FullForm of a complex number x+Iy is Complex:
Enter a complex number using the FullForm:
If the imaginary part is exactly zero, then the result is not Complex:
You have to use Re and Im to extract parts of Complex numbers:
Part does not work:
Enter a complex number with machine-number real and imaginary parts:
It is considered to be a machine number when both its real and imaginary parts are machine numbers:
Enter a complex number with arbitrary-precision real and imaginary parts:
The precision is based on the error in the complex plane:
Enter a complex number with an exact real part and an approximate imaginary part:
The exactness is kept in computations when possible:
can be used to stand for a complex number in a pattern:
A rule that switches real and imaginary parts:
An alternate definition:
 Applications   (1)
Define a function over the complexes by using functions defined over the reals:
Complexes are numbers:
Complexes are atomic objects with no subexpressions:
Use Complexes to indicate assumptions on domain conditions:
Numbers entered in the form x+Iy only become Complex numbers on evaluation:
The unevaluated form is expressed in terms of Plus and Times:
New in 1