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Le 25/02/2025 à 22:49, "Chris M. Thomasson" a écrit :I don't know what you mean here?On 2/25/2025 6:23 AM, Richard Hachel wrote:This is quite complicated, where I propose to use the nature of the imaginary number i in a somewhat particular way, and according to the new idea that i is not only defined by i²=-1 or i=sqrt(-1), but rather with the generalized idea that for all x, i^x=-1.x^4=-81>
>
What is x?
>
Try to forgive the floating point precision aspects, but, the roots are the r's, raising them to the 4'th power gives the p's:
_____________________
r0 = (2.12132,2.12132)
r1 = (-2.12132,2.12132)
r2 = (-2.12132,-2.12132)
r3 = (2.12132,-2.12132)
>
p0 = (-81,-7.08124e-06)
p1 = (-81,-1.93183e-06)
p2 = (-81,-7.53158e-05)
p3 = (-81,4.57051e-05)
_____________________
>
>
To gain a root, here is my code:
_____________________
ct_complex
root_calc(
ct_complex const& z,
int p,
int n
) {
float radius = std::pow(std::abs(z), 1.0 / p);
float angle_base = std::arg(z) / p;
float angle_step = (CT_PI * 2.0) / p;
float angle = angle = angle_step * n;
>
ct_complex c = {
std::cos(angle_base + angle) * radius,
std::sin(angle_base + angle) * radius
};
>
return c;
}
_____________________
>
>
Also, this is not using floating point for roots, just signed integers.
A bit like if this imaginary was the antithesis of 1 where for all x, then 1^x=1.
With this technique, we immediately have x=3i.
Date | Sujet | # | Auteur | |
25 Feb 25 | ![]() | 101 | Richard Hachel | |
25 Feb 25 | ![]() ![]() | 73 | Jim Burns | |
25 Feb 25 | ![]() ![]() ![]() | 72 | Richard Hachel | |
25 Feb 25 | ![]() ![]() ![]() ![]() | 3 | Python | |
25 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
25 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
25 Feb 25 | ![]() ![]() ![]() ![]() | 5 | guido wugi | |
25 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 4 | Richard Hachel | |
25 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Python | |
25 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Jim Burns | |
26 Feb 25 | ![]() ![]() ![]() ![]() | 21 | sobriquet | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 20 | sobriquet | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 16 | Moebius | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 12 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 11 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Moebius | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 8 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 6 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 5 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 4 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Moebius | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | sobriquet | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | sobriquet | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() | 42 | Jim Burns | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 41 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 39 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 38 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 37 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 36 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 5 | Python | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Richard Hachel | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Moebius | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 30 | efji | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 29 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Python | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Moebius | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 26 | joes | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 25 | Richard Hachel | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 4 | Jim Burns | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Jim Burns | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 19 | Chris M. Thomasson | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 17 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 16 | sobriquet | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 15 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 14 | sobriquet | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 13 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 12 | sobriquet | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 8 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 7 | efji | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Jim Burns | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Moebius | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Richard Hachel | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Moebius | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Chris M. Thomasson | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
27 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Jim Burns | |
25 Feb 25 | ![]() ![]() | 1 | Chris M. Thomasson | |
25 Feb 25 | ![]() ![]() | 5 | Chris M. Thomasson | |
25 Feb 25 | ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
25 Feb 25 | ![]() ![]() ![]() | 3 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
25 Feb 25 | ![]() ![]() | 19 | Chris M. Thomasson | |
25 Feb 25 | ![]() ![]() ![]() | 18 | Richard Hachel | |
25 Feb 25 | ![]() ![]() ![]() ![]() | 2 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() | 15 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() | 14 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | efji | |
28 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Chris M. Thomasson | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() | 5 | Barry Schwarz | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 3 | Moebius | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 2 | Richard Hachel | |
26 Feb 25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | 1 | Python | |
25 Feb 25 | ![]() ![]() | 1 | Barry Schwarz | |
28 Feb 25 | ![]() ![]() | 1 | Chris M. Thomasson |
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