NAME¶

std::polar(std::complex) - std::polar(std::complex)

Synopsis¶

Defined in header <complex>
template< class T >
std::complex<T> polar( const T& r, const T& theta = T() );

Returns a complex number with magnitude r and phase angle theta.

The behavior is undefined if r is negative or NaN, or if theta is infinite.

Parameters¶

r - magnitude
theta - phase angle

Return value¶

A complex number determined by r and theta.

Notes¶

std::polar(r, theta) is equivalent to any of the following expressions:

* r * std::exp(theta * 1i)
* r * (cos(theta) + sin(theta) * 1i)
* std::complex(r * cos(theta), r * sin(theta)).

Using polar instead of exp can be about 4.5x faster in vectorized loops.

Example¶

// Run this code

#include <cmath>
#include <complex>
#include <iomanip>
#include <iostream>
#include <numbers>
using namespace std::complex_literals;

int main()
{
constexpr auto π_2{std::numbers::pi / 2.0};
constexpr auto mag{1.0};

std::cout
<< std::fixed << std::showpos << std::setprecision(1)
<< " θ: │ polar: │ exp: │ complex: │ trig:\n";
for (int n{}; n != 4; ++n)
{
const auto θ{n * π_2};
std::cout << std::setw(4) << 90 * n << "° │ "
<< std::polar(mag, θ) << " │ "
<< mag * std::exp(θ * 1.0i) << " │ "
<< std::complex(mag * cos(θ), mag * sin(θ)) << " │ "
<< mag * (cos(θ) + 1.0i * sin(θ)) << '\n';
}
}

Output:¶

θ: │ polar: │ exp: │ complex: │ trig:
+0° │ (+1.0,+0.0) │ (+1.0,+0.0) │ (+1.0,+0.0) │ (+1.0,+0.0)
+90° │ (+0.0,+1.0) │ (+0.0,+1.0) │ (+0.0,+1.0) │ (+0.0,+1.0)
+180° │ (-1.0,+0.0) │ (-1.0,+0.0) │ (-1.0,+0.0) │ (-1.0,+0.0)
+270° │ (-0.0,-1.0) │ (-0.0,-1.0) │ (-0.0,-1.0) │ (-0.0,-1.0)

Defect reports

The following behavior-changing defect reports were applied retroactively to
previously published C++ standards.

DR Applied to Behavior as published Correct behavior
LWG 2459 C++98 behavior unclear for some inputs made undefined
LWG 2870 C++98 default value of parameter theta not dependent made dependent

See also¶

abs(std::complex) returns the magnitude of a complex number
(function template)
arg returns the phase angle
(function template)
exp(std::complex) complex base e exponential
(function template)