# std::polar(std::complex)

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< cpp‎ | numeric‎ | 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

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)

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