Re: Equation complexe

On 2/25/2025 4:39 PM, Chris M. Thomasson wrote:

On 2/25/2025 4:11 PM, Richard Hachel wrote:

Le 26/02/2025 à 00:48, "Chris M. Thomasson" a écrit :

On 2/25/2025 2:20 PM, Richard Hachel wrote:

Le 25/02/2025 à 23:08, "Chris M. Thomasson" a écrit :

On 2/25/2025 6:23 AM, Richard Hachel wrote:

x^4=-81
>
What is x?

[...]

x=-1.873444

>
To the 13'th power with higher precision:
>
roots[0] = (1.01898,0.251156)
roots[1] = (0.7855438,0.6959311)
roots[2] = (0.3721492,0.9812768)
roots[3] = (-0.1265003,1.041824)
roots[4] = (-0.5961701,0.8637015)
roots[5] = (-0.9292645,0.4877156)
roots[6] = (-1.049476,5.945845e-16)
roots[7] = (-0.9292645,-0.4877156)
roots[8] = (-0.5961701,-0.8637015)
roots[9] = (-0.1265003,-1.041824)
roots[10] = (0.3721492,-0.9812768)
roots[11] = (0.7855438,-0.6959311)
roots[12] = (1.01898,-0.251156)
>
raised[0] = (-1.873444,2.294307e-16)
raised[1] = (-1.873444,4.016197e-15)
raised[2] = (-1.873444,4.475059e-15)
raised[3] = (-1.873444,1.606015e-15)
raised[4] = (-1.873444,2.064877e-15)
raised[5] = (-1.873444,9.179548e-15)
raised[6] = (-1.873444,9.63841e-15)
raised[7] = (-1.873444,4.132072e-15)
raised[8] = (-1.873444,4.590934e-15)
raised[9] = (-1.873444,1.170561e-14)
raised[10] = (-1.873444,2.214818e-14)
raised[11] = (-1.873444,1.262333e-14)
raised[12] = (-1.873444,2.306591e-14)

>
I think that for the moment, we are making things terribly complicated.
If I ask you the cube root of 27?
Are you going to make a computer program?

 Huh? I use complex roots all the time, and yes, I have programs for it. How do you think I created my Multi Julia algorithm?
 http://www.paulbourke.net/fractals/multijulia/
 How would you implement my algo? I know how to do it for sure.

Btw, the cube root of 27+0i is:
roots[0] = (3,0)
roots[1] = (-1.5,2.598076)
roots[2] = (-1.5,-2.598076)