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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: =?ISO-8859-15?Q?y=3Df(x)=3D(x=B2)=B2+2x=B2+3?=
Date: Thu, 06 Feb 2025 16:44:59 -0500
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It happens that Chris M. Thomasson formulated :
> On 2/6/2025 12:52 PM, sobriquet wrote:
>> Op 06/02/2025 om 21:30 schreef Richard Hachel:
>>> Le 06/02/2025 à 20:15, sobriquet a écrit :
>>>> Op 06/02/2025 om 16:42 schreef Richard Hachel:
>>>>> Bonjour les amis !
>>>>>
>>>>> I asked for the roots of the following equation on the French forums, I 
>>>>> only got one answer that didn't satisfy me, and the rest is just 
>>>>> contempt and insults.
>>>>> So I'm trying my luck here.
>>>>>
>>>>> y=f(x)=(x²)²+2x²+3
>>>>>
>>>>> Il y a pour moi, deux racines très simples pour cette équation, dont 
>>>>> aucun n'est réelle.
>>>>>
>>>>> Can the Anglo-Saxons find these two roots?
>>>>>
>>>>> R.H.
>>>>>
>>>>
>>>> Actually there are four complex roots.
>>>>
>>>> https://www.wolframalpha.com/input?i=x%5E4%2B2x%5E2%2B3
>>>
>>> Yes, these are indeed the roots found in traditional development.
>>>
>>> Mathematicians find four complex roots.
>>>
>>> Personally, in this specific case, I only find two, because I think there 
>>> are only two.
>>>
>>> But I use different concepts, and a different method.
>>>
>>> For me, the roots are x'=-i and x"=i in this particular case, and I place 
>>> them on the y=0 axis, obviously, and on a simple Cartesian coordinate 
>>> system.
>>>
>>> DON'T SHOUT!
>>>
>>> I remind you that I use a different approach that I think is more correct 
>>> and in line with the very nature of i, and its precise definition, which 
>>> is not only i²=-1.
>>>
>>> R.H.
>> 
>> Ok, but that's a bit like people saying that 3 + 5 = 7 and then claiming 
>> that usually mathematicians say that 3 + 5 = 8, but they have different 
>> concepts that are more correct.
>
> Basically. :^)
>
>
>> Unless you're able to demonstrate that your alternative concepts are 
>> superior than the conventional way of defining these concepts, it
>> seems a bit silly.
>
> Ditto.
>
>
>> The concept of a complex number didn't fall from the sky.. it was developed 
>> over many centuries by multiple generations of mathematicians. So it seems 
>> unlikely that someone can come along and claim their way to conceive of a 
>> complex number is superior or more correct.
>
> For some reason, "some" people seem to want to say complex numbers are not 
> "real" because of the word "imaginary" used to define the y axis?

Some people thought (some still do) that the negative numbers aren't 
real either. Yet, there's no harm in pretending they are as long as 
correct answers are the result.