complex,
number,
t
The type complex includes all mathematical complex numbers
other than those included in the type rational.
Complexes are
expressed
in Cartesian form with a
real part and an imaginary part, each of which is a real.
The real part and imaginary part are either both
rational or both of the same float type.
The imaginary part can be a float zero, but can never
be a rational zero, for such a number is always represented
by Common Lisp as a rational rather than a complex.
Specializing.
(complex [typespec | *])
typespec—a type specifier that denotes a subtype of type real.
Every element of this type is a complex whose
real part and imaginary part are each of type
(upgraded-complex-part-type typespec).
This type encompasses those complexes
that can result by giving numbers of type typespec
to complex.
(complex type-specifier)
refers to all complexes that can result from giving
numbers of type type-specifier to the function complex,
plus all other complexes of the same specialized representation.
Section 12.1.5.3 (Rule of Canonical Representation for Complex Rationals), Section 2.3.2 (Constructing Numbers from Tokens), Section 22.1.3.1.4 (Printing Complexes)
The input syntax for a complex with real part r and
imaginary part i is #C(r i).
For further details, see Section 2.4 (Standard Macro Characters).
For every float, n, there is a complex
which represents the same mathematical number
and which can be obtained by (COERCE n 'COMPLEX).