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System Class COMPLEX

Class Precedence List

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.

Compound Type Specifier Kind


Compound Type Specifier Syntax

  • complex [typespec | *]

Compound Type Specifier Arguments

Compound Type Specifier Description

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.

See Also

  • {\secref\RuleOfCanonRepForComplexRationals}
  • {\secref\NumsFromTokens}, {\secref\PrintingComplexes}


The input syntax for a complex with real part r and imaginary part i is #C(r i). For further details, see section {\secref\StandardMacroChars}.

For every float, n, there is a complex which represents the same mathematical number and which can be obtained by (COERCE ''n'' 'COMPLEX).