Re: y=f(x)=(x²)²+2x²+3

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 !
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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.
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y=f(x)=(x²)²+2x²+3
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Il y a pour moi, deux racines très simples pour cette équation, dont aucun n'est réelle.
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Can the Anglo-Saxons find these two roots?
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R.H.
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Actually there are four complex roots.
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https://www.wolframalpha.com/input?i=x%5E4%2B2x%5E2%2B3

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Yes, these are indeed the roots found in traditional development.
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Mathematicians find four complex roots.
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Personally, in this specific case, I only find two, because I think there are only two.
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But I use different concepts, and a different method.
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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.
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DON'T SHOUT!
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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.
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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.

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Basically. :^)
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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.

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Ditto.
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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.

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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.