Re: Division of two complex numbers

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.