Re: Division of two complex numbers (is under-defined, like 0^0)

On 01/21/2025 11:46 AM, Richard Hachel wrote:

Le 21/01/2025 à 20:39, Ross Finlayson a écrit :

On 01/20/2025 03:02 AM, Richard Hachel wrote:

Division of two complex numbers.
>
Now let's set Z=(a+ib)/(a'+ib')
with
z1=a+ib
and
z2=a'+ib'
>
What becomes of Z=A+iB?
>
R.H.

>
Like I said, division of complex numbers is under-defined.
>
It's kind of like dividing by zero, about "roots of zero".

>
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544 / 5 000
If you want to know if a chosen mathematics is consistent, it is
necessary that Z=z1*z2 implies that z1=Z/z2 and that z2=Z/z1
>
We notice that the mathematics of mathematicians is consistent.
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Mine too.
>
Who relies on the best principles? It would seem that it is me.
>
For me, the problems posed remain true if we solve them differently, for
example with statistics (see the problem of the Plougastel college); for
me, the product of two orthogonal complexes is zero.
>
Mathematicians cannot do it.
>
R.H.

Well, one needn't necessarily employ the de-Moivre / Euler / Gauss
complex analysis for Euler's equation, nor necessarily, Gauss'
screw with regards to Wick rotation and such notions, the
de-Moivre / Euler / Gaussian "complex analysis", about the
usual notion of a diagram of complex numbers on the real number
plane, often referred to as "Argand" or "Wessel".
Here for example there's an inner sort of diagram called
the identity-dimension, x=y, then about all the functions
and their diagrams symmetric about x = y, and about their
diagrams in the octants, these elements of the identity
dimension about all the non-negative real domains in the
first quadrant.
Then, for example, there are two definitions of division
of complex numbers, that can sit off-side in quadrants
to the left and right as it were, left-complex and right-complex
numbers, a complex-complex diagram, and about an identity-dimension.
No one even talks about this, no one seems to even know that
such a thing exists, I just found it sitting there.
So, anyways, it's well known that division in complex numbers
is contrived, at best.
https://www.youtube.com/watch?v=Uv_6g__03_E&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=33
"Descriptive differential dynamics: complex numbers and the real field"