Some programming languages provide a complex data type for complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
storage and arithmetic as a built-in (primitive) data type
Data type
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
.
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
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
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
Compiler
A compiler is a computer program that transforms source code written in a programming language into another computer language...
into a sequence of floating-point machine instructions or into library
Library (computer science)
In computer science, a library is a collection of resources used to develop software. These may include pre-written code and subroutines, classes, values or type specifications....
calls. Those languages may also provide support for other operations, such as formatting, equality testing, etc. As in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, those languages often interpret a floating-point value as equivalent to a complex value with a zero imaginary part.
C99 is a modern dialect of the C programming language. It extends the previous version with new linguistic and library features, and helps implementations make better use of available computer hardware and compiler technology.-History:...
standard of the C programming language includes complex data types and complex math functions in the standard library header
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
standard library provides a complex templated class as well as complex math functions in the header
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
core module Math::Complex provides support for complex numbers
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
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 is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...
provides a Complex class in the standard library module complex
OCaml supports complex numbers with the standard library module Complex
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
supports complex numbers with the standard library module Complex
The Apache Commons Math library provides complex numbers for Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
: 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 is a software framework that runs primarily on Microsoft Windows. It includes a large library and supports several programming languages which allows language interoperability...
