Some programming languages provide a complex data type for complex number storage and arithmetic as a built-in (primitive) data type.
In some programming environments the term complex data type (in contrast to primitive data types) is a synonym to the composite data type.
Complex number arithmetic 
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.
Language support 
- The FORTRAN's type COMPLEX
- The C99 standard of the C programming language includes complex data types and complex math functions in the standard library header
- The C++ standard library provides a
complex templated class as well as complex math functions in the header
- 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
- 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)
- The Apache Commons Math library provides complex numbers for Java with its Complex class
- 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(0 1) ; 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 .NET Framework provides System.Numerics.Complex since version 4.0.
COMPLEX data type was provided in FORTRAN IV.