A complex variable or value is usually represented as a pair of floating point numbers. Languages that support a complex data type usually provide special syntax for building such values, and extend the basic arithmetic operations ('+', '−', '×', '÷') to act on them. These operations are usually translated by the compiler into a sequence of floating-point machine instructions or into library calls. Those languages may also provide support for other operations, such as formatting, equality testing, etc. As in mathematics, those languages often interpret a floating-point value as equivalent to a complex value with a zero imaginary part.
The C99 standard of the C programming language includes complex data types and complex math functions in the standard library header <complex.h>
The C++ standard library provides a complex templated class as well as complex math functions in the header <complex>
The Go programming language has built-in types complex64 (each component is 32-bit float) and complex128 (each component is 64-bit float)
The Perl core module Math::Complex provides support for complex numbers
Python support complex numbers built-in with the type complex. Imaginary number literals can be specified by appending a "j". Complex math functions are provided in the standard library module cmath
Ruby provides a Complex class in the standard library module complex
OCaml supports complex numbers with the standard library module Complex
Haskell supports complex numbers with the standard library module Data.Complex (previously called Complex)
Mercury provides complex numbers with full operator overloading support in the extras distribution, using libcomplex_numbers.
Java does not have a standard complex number class, but there exists a number of incompatible free implementations of a complex number class:
The Apache Commons Math library provides complex numbers for Java with its Complex class
jcomplexnumber is a project on implementation of complex number in Java
Common Lisp: The ANSI Common Lisp standard supports complex numbers of floats and arbitrary precision integers. Its basic mathematical functions are defined for complex numbers, where applicable. For example the square root of -1 is a complex number:
? (sqrt -1)
#C(01); the result of (sqrt -1)
Scheme: Complex numbers and functions (e.g. sin) are included in the language specification. Their implementation is however optional in the R5RS standard, while in R6RS is mandatory.
The smart BASIC for iOS naturally supports complex numbers in notation a + bi. Any variable, math operation or function can accept both real and complex numbers as arguments and return real or complex numbers depending on result. For example the square root of -4 is a complex number: