Standard library header <complex>

 

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This header is part of the numeric library.

Classes

complex

a complex number type (class template)

Functions

Operations
operator+operator-	applies unary operators to complex numbers (function template)
operator+operator-operator*operator/	performs complex number arithmetic 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 part (function template)
imag	returns the imaginary part (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 purely 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>&);
 
    // tuple interface:
    template<class T> struct tuple_size;
    template<size_t I, class T> struct tuple_element;
    template<class T> struct tuple_size<complex<T>>;
    template<size_t I, class T> struct tuple_element<I, complex<T>>;
    template<size_t I, class T>
      constexpr T& get(complex<T>&) noexcept;
    template<size_t I, class T>
      constexpr T&& get(complex<T>&&) noexcept;
    template<size_t I, class T>
      constexpr const T& get(const complex<T>&) noexcept;
    template<size_t I, class T>
      constexpr const T&& get(const complex<T>&&) noexcept;
 
    // 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&) = default;
    template<class X> constexpr explicit(/* see constructor page */)
        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>&);
};

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 79	C++98	the default argument of the second parameter of polar was missing in the synopsis	added