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Subject: Re: Division of two complex numbers
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Le 20/01/2025 à 17:23, Richard Hachel  a écrit :
> Le 20/01/2025 à 16:22, Richard Hachel  a écrit :
>> Le 20/01/2025 à 15:46, Moebius a écrit :
>>> Am 20.01.2025 um 12:02 schrieb Richard Hachel:
>>>> Division of two complex numbers.
>>>> 
>>>> Now let's set Z = (a + ib)/(a' + ib')
>>> 
>>> I guess you meant: Z = z1/z2
>>> 
>>>> with
>>>> z1 = a + ib
>>>> and
>>>> z2 = a' + ib'
>>>> 
>>>> What becomes of Z = A + iB?
>> 
>>> See here: 
>>> 
>>> https://en.wikipedia.org/wiki/Complex_number#Complex_conjugate,_absolute_value,_argument_and_division
>> 
>>  Merci beaucoup.
>> 
>>  I saw this.
>> 
>>  <http://nemoweb.net/jntp?EAsBh7E4-FgqHBbEPrgfaV9LEbI@jntp/Data.Media:1>
>> 
>>  Merci, je vais donc pouvoir répondre aux mathématiciens.
>> 
>>  R.H. 
> 
> As I expected, it is completely wrong.
> 
> The same sign error.
> 
> Mathematicians give:
> 
> z1/z2=[(aa'+bb')/(a'²+b'²)]+i[(ba'-ab')/(a'²+b'²)]
> 
> It was necessary to write:
> z1/z2=[(aa'-bb')/(a'²-b'²)]+i[(ba'-ab')/(a'²-b'²)]
> 
> Three sign errors (which is the same error) because each time we put i²=-1 
> where b and b' are already defined.
> 
> R.H. 

It is not an "error". Complex numbers are defined in such a way that this 
relation is true. They are what they are.

You cannot object to a "definition", except if it is not consistent. 
Definition of complex numbers is consistent, and they do have purposes. 
Quite a LOT of useful purposes, from geometry to integral calculus, 
electricity and quantum mechanics.

You can, nevertheless, propose that other rules for multiplication (so 
division) may be useful. But then you're not talking about complex numbers 
but another kind of numbers.

There are already other kinds of numbers build from pairs of real numbers, 
like dual numbers that are interesting. Dual numbers to name one. 

I'm not convinced that *your* proposition is useful. Maybe is is.

You are ridiculing yourself when you pretend that you "fix" a error in the 
definition of complex numbers, in an even more pathetic way than when you 
pretend to redefine Relativity.

But that is the story of your life, right? Making a fool of yourself and 
drown yourself in your pathetic mix of hubris and stupidity.