std::arg(std::complex)

 

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std::complex

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complex::complex complex::operator= complex::real complex::imag	complex::operator+=complex::operator-=complex::operator*=complex::operator/=
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operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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sin   cos tan asin (C++11) acos (C++11) atan (C++11)
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sinh   cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)
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tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

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