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Standard library header <complex>

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<algorithm>
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Numerics
<cfenv> (C++11)
<cmath>
<complex>
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Time
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<ccomplex> (C++11/17/20*)
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This header is part of the numeric library.

Contents

[edit] Classes

a complex number type
(class template)

[edit] Functions

Operations
applies unary operators to complex numbers
(function template) [edit]
performs complex number arithmetic on two complex values or a complex and a scalar
(function template) [edit]
(removed in C++20)
compares two complex numbers or a complex and a scalar
(function template) [edit]
serializes and deserializes a complex number
(function template) [edit]
returns the real part
(function template) [edit]
returns the imaginary part
(function template) [edit]
returns the magnitude of a complex number
(function template) [edit]
returns the phase angle
(function template) [edit]
returns the squared magnitude
(function template) [edit]
returns the complex conjugate
(function template) [edit]
(C++11)
returns the projection onto the Riemann sphere
(function template) [edit]
constructs a complex number from magnitude and phase angle
(function template) [edit]
Exponential functions
complex base e exponential
(function template) [edit]
complex natural logarithm with the branch cuts along the negative real axis
(function template) [edit]
complex common logarithm with the branch cuts along the negative real axis
(function template) [edit]
Power functions
complex power, one or both arguments may be a complex number
(function template) [edit]
complex square root in the range of the right half-plane
(function template) [edit]
Trigonometric functions
computes sine of a complex number (\({\small\sin{z}}\)sin(z))
(function template) [edit]
computes cosine of a complex number (\({\small\cos{z}}\)cos(z))
(function template) [edit]
computes tangent of a complex number (\({\small\tan{z}}\)tan(z))
(function template) [edit]
computes arc sine of a complex number (\({\small\arcsin{z}}\)arcsin(z))
(function template) [edit]
computes arc cosine of a complex number (\({\small\arccos{z}}\)arccos(z))
(function template) [edit]
computes arc tangent of a complex number (\({\small\arctan{z}}\)arctan(z))
(function template) [edit]
Hyperbolic functions
computes hyperbolic sine of a complex number (\({\small\sinh{z}}\)sinh(z))
(function template) [edit]
computes hyperbolic cosine of a complex number (\({\small\cosh{z}}\)cosh(z))
(function template) [edit]
computes hyperbolic tangent of a complex number (\({\small\tanh{z}}\)tanh(z))
(function template) [edit]
computes area hyperbolic sine of a complex number (\({\small\operatorname{arsinh}{z}}\)arsinh(z))
(function template) [edit]
computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z}}\)arcosh(z))
(function template) [edit]
computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z}}\)artanh(z))
(function template) [edit]
Literals
a std::complex literal representing purely imaginary number
(function) [edit]

[edit] 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);
 }
 }
}

[edit] 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>&);
};

[edit] 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

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