Defined in header <complex>
template< class T > 
T arg( const complex<T>& z );
long double arg( long double z );
(2) (since C++11)
template< class DoubleOrInteger >
double arg( DoubleOrInteger z );
(3) (since C++11)
float arg( float z );
(4) (since C++11)

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

(since C++11)Additional overloads are provided for float, double, long double, and all integer types, which are treated as complex numbers with zero imaginary component.


z - complex value

Return value

If no errors occur, returns the phase angle of z in the interval (−π; π).

Errors and special cases are handled as if the function is implemented as std::atan2(std::imag(z), std::real(z)).


#include <iostream>
#include <complex>
int main() 
    std::complex<double> z1(1, 0); 
    std::cout << "phase angle of " << z1 << " is " << std::arg(z1) << '\n';
    std::complex<double> z2(0, 1); 
    std::cout << "phase angle of " << z2 << " is " << std::arg(z2) << '\n';
    std::complex<double> z3(-1, 0); 
    std::cout << "phase angle of " << z3 << " is " << std::arg(z3) << '\n';
    std::complex<double> z4(-1, -0.0); 
    std::cout << "phase angle of " << z4 << " (the other side of the cut) is "
              << std::arg(z4) << '\n';


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

See also

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

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