Re: x²+4x+5=0

Am 24.01.2025 um 17:53 schrieb Python:

Le 24/01/2025 à 16:48, Richard Hachel  a écrit :

Le 24/01/2025 à 14:15, FromTheRafters a écrit :

Richard Hachel wrote :

The two imaginary roots are x'=-2-i and x"=-2+i.

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Shouldn't imaginary roots be on the y axis?

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Ce ne serait plus résoudre les racines de x, mais les racines de y quand y=0, ce qui est absurde.
Non, non, il s'agit de trouver les racines de x lorsque y=0.

 FromTheRafters was pointing out your misuse of the standard terminology.
 if x,y are real numbers, then x + iy is a complex numbers. The term "imaginary" (in French "imaginaire pur") denotes numbers of the form i*y. They are on the "y axis" refers to the representation of C as coordinates in the Euclidean plane.
 So "-2 - i" and "-2 + i" are not "imaginary".

But RH told us:
"[I] call these imaginary roots, because, since they do not exist, we must imagine them."
:-)