# std::arg(std::complex)

From cppreference.com
< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > T arg( const std::complex <T>& z ); | (1) |
Additional overloads (since C++11) |  |
Defined in header `<complex>` |  |
| (A) |
float arg( float f ); double arg( double f ); long double arg( long double f ); |  | (until C++23)
template< class FloatingPoint > FloatingPoint arg( FloatingPoint f ); |  | (since C++23)
template< class Integer > double arg( Integer i ); | (B) |

1) Calculates the phase angle (in radians) of the complex number z.

A,B) Additional overloads are provided for all integer and floating-point types, which are treated as complex numbers with zero imaginary component. | (since C++11)

### Parameters

z | - | complex value
f | - | floating-point value
i | - | integer value

### Return value

1) std::atan2 ( std::imag (z), std::real (z)). If no errors occur, this is the phase angle of z in the interval [−π; π].
A) Zero if f is positive or +0, π if f is negative or -0, NaN otherwise.
B) Zero if i is non-negative, π if it is negative.

### Notes

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their argument num:

- If num has a standard(until C++23) floating-point type `T`, then std::arg(num) has the same effect as std::arg( std::complex <T>(num)).
- Otherwise, if num has an integer type, then std::arg(num) has the same effect as std::arg( std::complex <double>(num)).

### Example

Run this code

    #include <complex>
    #include <iostream>

    int main()
    {
        std::complex<double> z1(1, 0);
        std::complex<double> z2(0, 0);
        std::complex<double> z3(0, 1);
        std::complex<double> z4(-1, 0);
        std::complex<double> z5(-1, -0.0);
        double f = 1.;
        int i = -1;

        std::cout << "phase angle of " << z1 << " is " << std::arg(z1) << '\n'
                  << "phase angle of " << z2 << " is " << std::arg(z2) << '\n'
                  << "phase angle of " << z3 << " is " << std::arg(z3) << '\n'
                  << "phase angle of " << z4 << " is " << std::arg(z4) << '\n'
                  << "phase angle of " << z5 << " is " << std::arg(z5) << " "
                     "(the other side of the cut)\n"
                  << "phase angle of " << f << " is " << std::arg(f) << '\n'
                  << "phase angle of " << i << " is " << std::arg(i) << '\n';

    }

Output:

    phase angle of (1,0) is 0
    phase angle of (0,0) is 0
    phase angle of (0,1) is 1.5708
    phase angle of (-1,0) is 3.14159
    phase angle of (-1,-0) is -3.14159 (the other side of the cut)
    phase angle of 1 is 0
    phase angle of -1 is 3.14159

### See also

abs(std::complex) | returns the magnitude of a complex number (function template)
polar | constructs a complex number from magnitude and phase angle (function template)
atan2atan2fatan2l (C++11)(C++11) | arc tangent, using signs to determine quadrants (function)
atan2(std::valarray) | applies the function std::atan2 to a valarray and a value (function template)
C documentation for carg

Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/complex/arg&oldid=154807"