# std::abs(std::complex)

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< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > T abs( const complex<T>& z ); |  |

Returns the magnitude of the complex number z.

### Parameters

z | - | complex value

### Return value

If no errors occur, returns the absolute value (also known as norm, modulus, or magnitude) of z.

Errors and special cases are handled as if the function is implemented as std::hypot(std::real(z), std::imag(z)).

### Example

Run this code

    #include <complex>
    #include <iostream>

    int main()
    {
        std::complex<double> z(1, 1);
        std::cout << z << " cartesian is rho = " << std::abs(z)
                  << " theta = " << std::arg(z) << " polar\n";
    }

Output:

    (1,1) cartesian is rho = 1.41421 theta = 0.785398 polar

### See also

arg | returns the phase angle (function template)
polar | constructs a complex number from magnitude and phase angle (function template)
abs(int)labs llabs (C++11) | computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
abs(float)fabs fabsf fabsl (C++11)(C++11) | absolute value of a floating point value (\(\small{|x|}\)|x|) (function)
hypot hypotf hypotl (C++11)(C++11)(C++11) | computes square root of the sum of the squares of two or three (since C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√x2 +y2 +z2 ) (since C++17) (function)
abs(std::valarray) | applies the function abs to each element of valarray (function template)

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