Re: Equation complexe

Le 26/02/2025 à 20:10, Richard Hachel a écrit :

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.

Consistent, but without relation with complex numbers and useless.

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.

At least your previous system were consistent, it was not at all describing complex numbers, but it was consistent as a ring (not a field, so irrelevant when it comes to what complex numbers allows).
Your new "system" with i^2 = -1 and i^4 = -1 is not even consistent. It can be shown contradictory in one line. [note that this systems is NOT the previous one you proposed at all]
Meanwhile you still fail to understand what complex numbers are, why they are consistent, useful and used for: you are drowning yourself in stupidity, ignorance and arrogance. You persist in lies and hypocrisy. In other words: the story of your life.