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

 

C++

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Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

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!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
log   log10   exp
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)
Helper types
tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

(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 <complex>
#include <iostream>
 
int main()
{
    std::complex<double> c2(2.0, 0.0);
    std::complex<double> ci(0.0, 1.0);
 
    std::cout << ci << " + " << c2 << " = " << ci + c2 << '\n'
              << ci << " * " << ci << " = " << ci * ci << '\n'
              << ci << " + " << c2 << " / " << ci << " = " << ci + c2 / ci << '\n'
              << 1  << " / " << ci << " = " << 1.0 / ci << '\n';
 
//    std::cout << 1.0f / 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)