# 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))

### Examples

Run this code

    #include <iostream>
    #include <complex>

    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 (|x|) (function)
abs(float)fabs fabsf fabsl (C++11)(C++11) | absolute value of a floating point value (|x|) (function)
hypot hypotf hypotl (C++11)(C++11)(C++11) | computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function)
abs(std::valarray) | applies the function std::abs to each element of valarray (function template)

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