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Subject: Re: Equation complexe
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Date: Wed, 26 Feb 25 19:10:47 +0000
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From: Richard Hachel <r.hachel@tiscali.fr>

Le 26/02/2025 à 19:48, Python a écrit :
> In your previous "system", this was false: there were divisors of 0 i.e. 
> non-zero items z1, z2 such as z1*z2 = 0. You didn't even notice it first, I 
> pointed it out it on fr.sci.maths.

This is entirely correct.
And you were absolutely right to point this out.
In the Hachel system, we have Z=z1+z2=(a+a')+i(b+b').
Which is consistent with the traditional mathematical system.
But we do not have Z=z1.z2=(aa'-bb')+i(ab'+a'b)
but Z=z1.z2=(aa'+bb')+i(ab'+a'b).
So far no problem, it may be wrong (which I don't think),
but it is consistent.
Now, the inverse operation which is the quotient, will obviously also be 
upset, and, we have, in the Hachel formula a divisor a'+ib' which will 
induce in the denominator a'²-b'².
This is what Jean-Paul Messager noticed. What does this mean?
This means that, for example, you cannot divide a complex by another 
complex of type a'+ib' if a'=b'.
On the surface, it may sound funny to say that you cannot divide a complex 
by 5+5i for example.
But it makes sense.
This amounts to dividing by zero without us realizing it.

R.H.