std::arg(std::complex)(3)

NAME
std::arg(std::complex) - std::arg(std::complex)

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

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)
   atan2
   atan2f arc tangent, using signs to determine quadrants
   atan2l (function)
   (C++11)
   (C++11)
   atan2(std::valarray) applies the function std::atan2 to a valarray and a value
                        (function template)
   C documentation for
   carg