Standard library header <complex>

 

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Standard Library headers

Note: a slash '/' in a revision mark means that the header was deprecated and/or removed.

Language Support
<cstddef> <cstdlib> <version> (C++20) <limits> <climits>	<cfloat> <cstdint> (C++11) <new> <typeinfo>	<source_location> (C++20) <exception> <initializer_list> (C++11)   <compare> (C++20)	<coroutine> (C++20) <csignal> <csetjmp> <cstdarg>
Concepts
<concepts> (C++20)
Diagnostics
<stdexcept>	<cassert>	<cerrno>	<system_error> (C++11)
General utilities
<utility> <memory> <memory_resource> (C++17) <scoped_allocator> (C++11)   <expected> (C++23)	<bitset> <tuple> (C++11) <optional> (C++17) <any> (C++17)	<variant> (C++17) <type_traits> (C++11) <ratio> (C++11) <chrono> (C++11)	<typeindex> (C++11) <functional> <stacktrace> (C++23) <ctime>
Strings
<string> <string_view> (C++17) <cstring>	<charconv> (C++17) <format> (C++20)	<cctype> <cwctype>	<cwchar> <cuchar> (C++11)
Localization
<locale> <clocale>	<codecvt> (C++11/17)
Containers
<span> (C++20) <array> (C++11) <vector>	<deque> <forward_list> (C++11) <list>	<map> <set> <queue>	<unordered_map> (C++11) <unordered_set> (C++11) <stack>
Iterators
<iterator>
Ranges
<ranges> (C++20)
Algorithms
<algorithm>	<execution> (C++17)
Numerics
<complex> <random> (C++11)	<valarray> <numeric>	<bit> (C++20) <numbers> (C++20)	<cfenv> (C++11) <cmath>
Input/Output
<iosfwd> <ios> <iomanip> <streambuf>	<istream> <ostream> <iostream>	<syncstream> (C++20) <spanstream> (C++23) <sstream> <fstream>	<cstdio> <cinttypes> (C++11) <strstream> (C++98/)
Regular expressions
<regex> (C++11)
Filesystem support
<filesystem> (C++17)
Thread support
<thread> (C++11) <atomic> (C++11) <mutex> (C++11)	<shared_mutex> (C++14) <condition_variable> (C++11)   <future> (C++11)	<stop_token> (C++20) <semaphore> (C++20)	<latch> (C++20) <barrier> (C++20)
C compatibility
<cstdbool> (C++11/17/20) <ccomplex> (C++11/17/20)	<ctgmath> (C++11/17/20) <cstdalign> (C++11/17/20)	<ciso646> (until C++20) <stdatomic.h>

 

This header is part of the numeric library.

Classes

complex	a complex number type (class template)
complex<float>complex<double>complex<long double>	a complex number type (class template specialization)

Functions

Operations
operator+operator-	applies unary operators to complex numbers (function template)
operator+operator-operator*operator/	performs complex number arithmetics on two complex values or a complex and a scalar (function template)
operator==operator!= (removed in C++20)	compares two complex numbers or a complex and a scalar (function template)
operator<<operator>>	serializes and deserializes a complex number (function template)
real	returns the real component (function template)
imag	returns the imaginary component (function template)
abs(std::complex)	returns the magnitude of a complex number (function template)
arg	returns the phase angle (function template)
norm	returns the squared magnitude (function template)
conj	returns the complex conjugate (function template)
proj (C++11)	returns the projection onto the Riemann sphere (function template)
polar	constructs a complex number from magnitude and phase angle (function template)
Exponential functions
exp(std::complex)	complex base e exponential (function template)
log(std::complex)	complex natural logarithm with the branch cuts along the negative real axis (function template)
log10(std::complex)	complex common logarithm with the branch cuts along the negative real axis (function template)
Power functions
pow(std::complex)	complex power, one or both arguments may be a complex number (function template)
sqrt(std::complex)	complex square root in the range of the right half-plane (function template)
Trigonometric functions
sin(std::complex)	computes sine of a complex number (\({\small\sin{z} }\)sin(z)) (function template)
cos(std::complex)	computes cosine of a complex number (\({\small\cos{z} }\)cos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (\({\small\tan{z} }\)tan(z)) (function template)
asin(std::complex) (C++11)	computes arc sine of a complex number (\({\small\arcsin{z} }\)arcsin(z)) (function template)
acos(std::complex) (C++11)	computes arc cosine of a complex number (\({\small\arccos{z} }\)arccos(z)) (function template)
atan(std::complex) (C++11)	computes arc tangent of a complex number (\({\small\arctan{z} }\)arctan(z)) (function template)
Hyperbolic functions
sinh(std::complex)	computes hyperbolic sine of a complex number (\({\small\sinh{z} }\)sinh(z)) (function template)
cosh(std::complex)	computes hyperbolic cosine of a complex number (\({\small\cosh{z} }\)cosh(z)) (function template)
tanh(std::complex)	computes hyperbolic tangent of a complex number (\({\small\tanh{z} }\)tanh(z)) (function template)
asinh(std::complex) (C++11)	computes area hyperbolic sine of a complex number (\({\small\operatorname{arsinh}{z} }\)arsinh(z)) (function template)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z} }\)arcosh(z)) (function template)
atanh(std::complex) (C++11)	computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z} }\)artanh(z)) (function template)
Literals
operator""ifoperator""ioperator""il (C++14)	A std::complex literal representing pure imaginary number (function)

Synopsis

namespace std {
 
    template<class T> class complex;
 
    template<> class complex<float>;
    template<> class complex<double>;
    template<> class complex<long double>;
 
    // operators:
    template<class T> constexpr complex<T> operator+(
        const complex<T>&, const complex<T>&);
    template<class T> constexpr complex<T> operator+(const complex<T>&, const T&);
    template<class T> constexpr complex<T> operator+(const T&, const complex<T>&);
 
    template<class T> constexpr complex<T> operator-(
        const complex<T>&, const complex<T>&);
    template<class T> constexpr complex<T> operator-(const complex<T>&, const T&);
    template<class T> constexpr complex<T> operator-(const T&, const complex<T>&);
 
    template<class T> constexpr complex<T> operator*(
        const complex<T>&, const complex<T>&);
    template<class T> constexpr complex<T> operator*(const complex<T>&, const T&);
    template<class T> constexpr complex<T> operator*(const T&, const complex<T>&);
 
    template<class T> constexpr complex<T> operator/(
        const complex<T>&, const complex<T>&);
    template<class T> constexpr complex<T> operator/(const complex<T>&, const T&);
    template<class T> constexpr complex<T> operator/(const T&, const complex<T>&);
 
    template<class T> constexpr complex<T> operator+(const complex<T>&);
    template<class T> constexpr complex<T> operator-(const complex<T>&);
 
    template<class T> constexpr bool operator==(
        const complex<T>&, const complex<T>&);
    template<class T> constexpr bool operator==(const complex<T>&, const T&);
    template<class T> constexpr bool operator==(const T&, const complex<T>&);
 
    template<class T> constexpr bool operator!=(const complex<T>&, const complex<T>&);
    template<class T> constexpr bool operator!=(const complex<T>&, const T&);
    template<class T> constexpr bool operator!=(const T&, const complex<T>&);
 
    template<class T, class charT, class traits>
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>&, complex<T>&);
 
    template<class T, class charT, class traits>
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>&, const complex<T>&);
 
    // values:
    template<class T> constexpr T real(const complex<T>&);
    template<class T> constexpr T imag(const complex<T>&);
 
    template<class T> T abs(const complex<T>&);
    template<class T> T arg(const complex<T>&);
    template<class T> constexpr T norm(const complex<T>&);
 
    template<class T> constexpr complex<T> conj(const complex<T>&);
    template<class T> complex<T> proj(const complex<T>&);
    template<class T> complex<T> polar(const T&, const T& = 0);
 
    // transcendentals:
    template<class T> complex<T> acos(const complex<T>&);
    template<class T> complex<T> asin(const complex<T>&);
    template<class T> complex<T> atan(const complex<T>&);
 
    template<class T> complex<T> acosh(const complex<T>&);
    template<class T> complex<T> asinh(const complex<T>&);
    template<class T> complex<T> atanh(const complex<T>&);
 
    template<class T> complex<T> cos  (const complex<T>&);
    template<class T> complex<T> cosh (const complex<T>&);
    template<class T> complex<T> exp  (const complex<T>&);
    template<class T> complex<T> log  (const complex<T>&);
    template<class T> complex<T> log10(const complex<T>&);
 
    template<class T> complex<T> pow(const complex<T>&, const T&);
    template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
    template<class T> complex<T> pow(const T&, const complex<T>&);
 
    template<class T> complex<T> sin    (const complex<T>&);
    template<class T> complex<T> sinh   (const complex<T>&);
    template<class T> complex<T> sqrt   (const complex<T>&);
    template<class T> complex<T> tan    (const complex<T>&);
    template<class T> complex<T> tanh   (const complex<T>&);
 
    // complex literals:
    inline namespace literals {
    inline namespace complex_literals {
        constexpr complex<long double> operator""il(long double);
        constexpr complex<long double> operator""il(unsigned long long);
        constexpr complex<double> operator""i(long double);
        constexpr complex<double> operator""i(unsigned long long);
        constexpr complex<float> operator""if(long double);
        constexpr complex<float> operator""if(unsigned long long);
    }
    }
}

Class std::complex

template<class T>
class complex {
public:
    typedef T value_type;
    constexpr complex(const T& re = T(), const T& im = T());
    constexpr complex(const complex&);
    template<class X> constexpr complex(const complex<X>&);
 
    constexpr T real() const;
    constexpr void real(T);
    constexpr T imag() const;
    constexpr void imag(T);
 
    constexpr complex<T>& operator= (const T&);
    constexpr complex<T>& operator+=(const T&);
    constexpr complex<T>& operator-=(const T&);
    constexpr complex<T>& operator*=(const T&);
    constexpr complex<T>& operator/=(const T&);
 
    constexpr complex& operator=(const complex&);     
    template<class X> constexpr complex<T>& operator= (const complex<X>&);   
    template<class X> constexpr complex<T>& operator+=(const complex<X>&);   
    template<class X> constexpr complex<T>& operator-=(const complex<X>&);   
    template<class X> constexpr complex<T>& operator*=(const complex<X>&);   
    template<class X> constexpr complex<T>& operator/=(const complex<X>&);   
 
};

std::complex specializations

template<> class complex<float> {
public:
    typedef float value_type;
 
    constexpr complex(float re = 0.0f, float im = 0.0f);
    explicit constexpr complex(const complex<double>&);
    explicit constexpr complex(const complex<long double>&);
 
    constexpr float real() const;
    constexpr void real(float);
    constexpr float imag() const;
    constexpr void imag(float);
 
    constexpr complex<float>& operator= (float);
    constexpr complex<float>& operator+=(float);
    constexpr complex<float>& operator-=(float);
    constexpr complex<float>& operator*=(float);
    constexpr complex<float>& operator/=(float);
 
    constexpr complex<float>& operator=(const complex<float>&);
    template<class X> constexpr complex<float>& operator= (const complex<X>&);
    template<class X> constexpr complex<float>& operator+=(const complex<X>&);
    template<class X> constexpr complex<float>& operator-=(const complex<X>&);
    template<class X> constexpr complex<float>& operator*=(const complex<X>&);
    template<class X> constexpr complex<float>& operator/=(const complex<X>&);
};
 
template<> class complex<double> {
public:
    typedef double value_type;
 
    constexpr complex(double re = 0.0, double im = 0.0);
    constexpr complex(const complex<float>&);
    explicit constexpr complex(const complex<long double>&);
 
    constexpr double real() const;
    constexpr void real(double);
    constexpr double imag() const;
    constexpr void imag(double);
 
    constexpr complex<double>& operator= (double);
    constexpr complex<double>& operator+=(double);
    constexpr complex<double>& operator-=(double);
    constexpr complex<double>& operator*=(double);
    constexpr complex<double>& operator/=(double);
 
    constexpr complex<double>& operator=(const complex<double>&);
    template<class X> constexpr complex<double>& operator= (const complex<X>&);
    template<class X> constexpr complex<double>& operator+=(const complex<X>&);
    template<class X> constexpr complex<double>& operator-=(const complex<X>&);
    template<class X> constexpr complex<double>& operator*=(const complex<X>&);
    template<class X> constexpr complex<double>& operator/=(const complex<X>&);
};
 
template<> class complex<long double> {
public:
    typedef long double value_type;
 
    constexpr complex(long double re = 0.0L, long double im = 0.0L);
    constexpr complex(const complex<float>&);
    constexpr complex(const complex<double>&);
 
    constexpr long double real() const;
    constexpr void real(long double);
    constexpr long double imag() const;
    constexpr void imag(long double);
 
    constexpr complex<long double>& operator=(const complex<long double>&);
    constexpr complex<long double>& operator= (long double);
    constexpr complex<long double>& operator+=(long double);
    constexpr complex<long double>& operator-=(long double);
    constexpr complex<long double>& operator*=(long double);
    constexpr complex<long double>& operator/=(long double);
 
    template<class X> constexpr complex<long double>& operator= (const complex<X>&);
    template<class X> constexpr complex<long double>& operator+=(const complex<X>&);
    template<class X> constexpr complex<long double>& operator-=(const complex<X>&);
    template<class X> constexpr complex<long double>& operator*=(const complex<X>&);
    template<class X> constexpr complex<long double>& operator/=(const complex<X>&);
 
};