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std::polar(std::complex)

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

#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