Re: Equation complexe

On 2/27/2025 1:42 PM, Richard Hachel wrote:

Le 27/02/2025 à 21:53, Jim Burns a écrit :

On 2/27/2025 2:35 PM, Jim Burns wrote:

 

There is a very nice formula expressing all this.
𝑒ⁱᶿ = sin(θ) + 𝑖⋅cos(θ)

 

D'oh!

 

𝑒ⁱᶿ = cos(θ) + 𝑖⋅sin(θ)

 Yes, it's more better. :))

To gain n-ary roots of a target complex number, keep in mind that the power is a signed integer here:
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ct_complex
root_calc(
     ct_complex const& z,
     int p,
     int n
) {
     ct_real radius = std::pow(std::abs(z), 1.f / p);
     ct_real angle_base = std::arg(z) / p;
     ct_real angle_step = CT_PI2 / p;
     ct_real angle = angle = angle_step * n;
     ct_complex c = {
         std::cos(angle_base + angle) * radius,
         std::sin(angle_base + angle) * radius
     };
     return c;
}
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