Built-in Mathematica Symbol

Complex

Complex
is the head used for complex numbers.

Enter a complex number:

Complex is the Head for complex numbers:

Enter a complex number:

Complex is the Head for complex numbers:

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[x, y]:

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:

_Complex can be used to stand for a complex number in a pattern:

A rule that switches real and imaginary parts:

An alternate definition:

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: