Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Equation complexe
Date: Tue, 25 Feb 2025 17:59:11 -0800
Organization: A noiseless patient Spider
Lines: 87
Message-ID: <vplshg$28ulv$1@dont-email.me>
References: <oAvE_mEWK82aUJOdwpGna1Rzs1U@jntp> <vplf03$26m33$2@dont-email.me>
 <phaAQGQzp-zUFaCH1je-PMrkpYE@jntp> <vplkro$27sv3$1@dont-email.me>
 <BemyjeEyCW-MjW40qw4k1u6D-7E@jntp> <vplnji$27sv3$3@dont-email.me>
 <xJwIPBS44lg0ns4JZKgLPustB5M@jntp>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 26 Feb 2025 02:59:12 +0100 (CET)
Injection-Info: dont-email.me; posting-host="7d2bb58dfe24acf4c8e5f08fe35a4e41";
	logging-data="2390719"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18y7YvNUR6iaLRxDgAeZhKttRrJVzspTRA="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:PZkXEoPThBrekV/3TZo2KQA7Ago=
In-Reply-To: <xJwIPBS44lg0ns4JZKgLPustB5M@jntp>
Content-Language: en-US
Bytes: 4098

On 2/25/2025 5:11 PM, Richard Hachel wrote:
> Le 26/02/2025 à 01:34, "Chris M. Thomasson" a écrit :
>> On 2/25/2025 4:11 PM, Richard Hachel wrote:
>>>> 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?
>>> Why make a computer program if I ask you the fourth root of -81?
>>>
>>> The answer is simple and obvious. x=3i.
>>
>> The fourth root of -81+0i wrt power of 4 is *:
>>
>> roots[0] = (2.12132,2.12132)
>> roots[1] = (-2.12132,2.12132)
>> roots[2] = (-2.12132,-2.121321)
>> *roots[3] = (2.12132,-2.121321)
>>
>> I don't know what you x=3i even means right now. Any of these roots 
>> raised to the 4'th power equals -81+0i.
> 
> We are not talking about the same thing, nor are we using the same 
> mathematics.
> 
> If I ask what are the complex roots of f(x)=x²+4x+5,
> you will tell me that we must use [-b$sqrt(b²-4ac)]/2a using i.
> 
> And you will give me x'=-2+i and x"=-2-i.
> 
> Coordinates on x'Ox that I will immediately place in A(-3,0) and B(-1,0) 
> and which are the imaginary roots on y=0, the equation having no real 
> roots.
> 
> Well, I do the same to find the fourth root of -81.
> 
> x^4=-81.
> 
> For me, i ^x=-1 whatever 1.
> 
> x^4=-81 ---> x^4=-(i^4)(-81)=81(i^4)
> x=3i

List out all of the four roots of -81+0i using your system such that 
when they are raised to the 4'th power equal -81. I know how to find 
them using good ol' complex numbers.





> 
> Conversely, x^4=(3i)^4 = 81(i^4) with i^4=-1 by definition of i for me.
> 
> But that has nothing to do with the Argand frame, which is something 
> completely different.
> 
> R.H.