Dirk Van de moortel wrote:
> "The TimeLord" <mathnphysics-not@bellsouth.net> wrote in message news:UqWdnes_svgUJzHfRVn-gQ@comcast.com...
> > Don Giovanni <laterel0328@yahoo.com> wrote in
> > <1118580874.108666.125200@g49g2000cwa.googlegroups.com> on Sunday 12 June
> > 2005 07:54 posted to sci.physics.relativity:
> >
> > > i never understod whay complex
> > > number only have two dimenssion,
> > > the real and imaginary part
> > >
> > >
> > > whay not more?
> >
> > Actually they don't have two dimensions either. A dimension is defined as
> > the number of linearly independent basis vectors that span a space. I know
> > that sounds trite, but my point is that in understanding things like
> > complex numbers, you need to understand how mathematicians define things.
> >
> > So, a complex number is a number that when multiplied by itself equals a
> > real number.
>
> That is wrong.
> A complex number multiplied by itself does not give a real number.
> It gives a compex number:
> Having x and y real numbers,
>     ( x + y i )^2 = x^2 - y^2 + 2 x y i
> Only if x = 0 will the result be a real number, i.o.w. a strictly
> imaginary number multiplied by itself gives a real number.

wrong, only if the imaginary part or the real part are zero

>
> > As long as the real number is positive, another real will do
> > as in Sqrt[4]=+-2; both real. If the real is negative then you get the
> > imaginary part as in Sqrt[-4]=+-2i.
>
> That is wrong as well.
>     sqrt(4) = 2
>     - sqrt(4) = - 2
>     sqrt(-4) is nonsense

wrong, sqrt(-4) = sqrt(-1*4) = sqrt(-1)*sqrt(4) = i4,
which is complex pure imaginary

> Sqrt is a function defined for positive real numbers only.
> The result is a positive real number (and positive includes zero).

wrong fool

>
> What you *can* write however, is this:
>     sqrt( x^2 ) = +- x
> which is an abbreviation for the statement:
>     |        sqrt( x^2 ) = x    (namely for all real x >= 0)
>     |           or
>     |        sqrt( x^2 ) = -x    (namely for all real x <= 0)
> You can write this because in both cases the argument and the
> result of the function are positive values
> Which one of both equations is valid, depends on the sign
> of x. That is why you *cannot* write
>     sqrt( 4 ) = +- 2
> since the case with -2 can never occur.

bullshitisimo