operator+,-,*,/ (std::complex)

C++

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Technical Specifications

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

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iota (C++11)

accumulate

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bit_cast (C++20)

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

(1)

template< class T > std::complex<T> operator+( const std::complex<T>& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator+( const std::complex<T>& lhs, const std::complex<T>& rhs);

(since C++20)

(2)

template< class T > std::complex<T> operator+( const std::complex<T>& lhs, const T& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator+( const std::complex<T>& lhs, const T& rhs);

(since C++20)

(3)

template< class T > std::complex<T> operator+( const T& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator+( const T& lhs, const std::complex<T>& rhs);

(since C++20)

(4)

template< class T > std::complex<T> operator-( const std::complex<T>& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator-( const std::complex<T>& lhs, const std::complex<T>& rhs);

(since C++20)

(5)

template< class T > std::complex<T> operator-( const std::complex<T>& lhs, const T& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator-( const std::complex<T>& lhs, const T& rhs);

(since C++20)

(6)

template< class T > std::complex<T> operator-( const T& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator-( const T& lhs, const std::complex<T>& rhs);

(since C++20)

(7)

template< class T > std::complex<T> operator*( const std::complex<T>& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator*( const std::complex<T>& lhs, const std::complex<T>& rhs);

(since C++20)

(8)

template< class T > std::complex<T> operator*( const std::complex<T>& lhs, const T& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator*( const std::complex<T>& lhs, const T& rhs);

(since C++20)

(9)

template< class T > std::complex<T> operator*( const T& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator*( const T& lhs, const std::complex<T>& rhs);

(since C++20)

(10)

template< class T > std::complex<T> operator/( const std::complex<T>& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator/( const std::complex<T>& lhs, const std::complex<T>& rhs);

(since C++20)

(11)

template< class T > std::complex<T> operator/( const std::complex<T>& lhs, const T& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator/( const std::complex<T>& lhs, const T& rhs);

(since C++20)

(12)

template< class T > std::complex<T> operator/( const T& lhs, const std::complex<T>& rhs);

(until C++20)

template< class T > constexpr std::complex<T> operator/( const T& lhs, const std::complex<T>& rhs);

(since C++20)

Implements the binary operators for complex arithmetic and for mixed complex/scalar arithmetic. Scalar arguments are treated as complex numbers with the real part equal to the argument and the imaginary part set to zero.

1-3) Returns the sum of its arguments

4-6) Returns the result of subtracting rhs from lhs

7-9) Multiplies its arguments

10-12) Divides lhs by rhs

Parameters

lhs, rhs

-

the arguments: either both complex numbers or one complex and one scalar of matching type (float, double, long double)

Return value

1-3) std::complex<T>(lhs) += rhs

4-6) std::complex<T>(lhs) -= rhs

7-9) std::complex<T>(lhs) *= rhs

10-12) std::complex<T>(lhs) /= rhs

Notes

Because template argument deduction does not consider implicit conversions, these operators cannot be used for mixed integer/complex arithmetic. In all cases, the scalar must have the same type as the underlying type of the complex number.

The GCC flag "-fcx-limited-range" (included by "-ffast-math") changes the behavior of complex multiply/division by removing checks for floating point edge cases. This impacts loop vectorization.

Example

Run this code

#include <iostream>
#include <complex>
int main()
{
    std::complex<double> c2(2, 0);
    std::complex<double> ci(0, 1);

    std::cout << ci << " + " << c2 << " = " << ci+c2 << '\n'
              << ci << " * " << ci << " = " << ci*ci << '\n'
              << ci << " + " << c2 << " / " << ci << " = " << ci+c2/ci << '\n'
              << 1  << " / " << ci << " = " << 1./ci << '\n';

//    std::cout << 1.f/ci; // compile error
//    std::cout << 1/ci; // compile error
}

Output:

(0,1) + (2,0) = (2,1)
(0,1) * (0,1) = (-1,0)
(0,1) + (2,0) / (0,1) = (0,-1)
1 / (0,1) = (0,-1)

See also

operator+=operator-=operator/=operator*=	compound assignment of two complex numbers or a complex and a scalar (public member function)
operator+operator-	applies unary operators to complex numbers (function template)