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