Re: complex numbers


"N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@xxxxxxxxxx> wrote in message news:5%Vre.2$eV4.1@xxxxxxxxxxxxx
> Dear Dirk Van de moortel:
>
> "Dirk Van de moortel"
> <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
> news:1URre.121077$%81.6970506@xxxxxxxxxxxxxxxxxxxxxxxx
> >
> > "N:dlzc D:aol T:com (dlzc)" <N: dlzc1 D:cox T:net@xxxxxxxxxx>
> > wrote in message news:f4Nre.204$kk.43@xxxxxxxxxxxxx
> ...
> >> *BUT*
> >> -1 = i^2 =[+/-sqrt(-1)] * [+/-sqrt(-1)]
> >
> > No, don't do that. Whenever you write +/-, you write two
> > equations.
> > When someone writes, for example as a result of a calculation
> > "x = +/- 10"
> > this is nothing more than a *shortcut* of the statement
> > "x = 10 or x = -10" .
> >
> > When you write
> > -1 = i^2 =[+/-sqrt(-1)] * [+/-sqrt(-1)] ,
> > you have 4 equations:
> > -1 = i^2 = sqrt(-1) * sqrt(-1) or
> > -1 = i^2 = sqrt(-1) * (-sqrt(-1)) or
> > -1 = i^2 = (-sqrt(-1)) *sqrt(-1) or
> > -1 = i^2 = (-sqrt(-1)) *(-sqrt(-1))
> > Apart from the fact that writing sqrt(-1) is wrong, but
> > assuming for 5 seconds it *would* be okay, clearly
> > the second and the third equations are just plain wrong.
>
> Actually, the second and third equations give the *correct*
> result, if you follw Androcles' logic from there on:
> -1 = i^2 = sqrt(-1) * (-sqrt(-1))
> therefore
> -1 = i^2 = -(sqrt( -1 * -1 )) = -1

AAAARG - Androcles' logic. You are so cruel!

> It seems a little arbitrary to "invert the sign choices" when
> "ingesting" the two options, which is simply saying that pairs of
> such are negative...
>
> Arbitrary, ad hoc. For-ged-abou-dit.

Who could ever forget Androcles? ;-)

Cheers,
Dirk Vdm


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