Re: complex numbers



Dirk Van de moortel wrote:
> "The TimeLord" <mathnphysics-not@xxxxxxxxxxxxx> wrote in message news:UqWdnes_svgUJzHfRVn-gQ@xxxxxxxxxxxxxx
> > Don Giovanni <laterel0328@xxxxxxxxx> wrote in
> > <1118580874.108666.125200@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> 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

>
> >
> > So then, the answer to your question is that real numbers can be positive or
> > negative, so you need both real and imaginary parts of complex numbers to
> > describe them. The real part describes the square root of the positive and
> > the imaginary part describes the square root of the negative.
>
> The last sentence sounds like nonsense.
>
> >
> > To really get a feel for this, consider...
> > i = Sqrt[-1]
> > So i^2 = -1
> > So i^4 = 1
> > But
> > Sqrt[1] = +-1
> > So Sqrt[i^4] = +-1
> > So i^2 = +-1 since Sqrt[i^4]=(i^4)^(1/2)
> >
> > You can see that unless you keep straight just what the square root is
> > defined to be, you can go very far afield by continuing the square roots to
> > result in i=1, which is nonsense.
>
> Indeed, that is why one should never
> - put anything but positive numbers under the square root sign.
> - write something like sqrt(4) = +- 2

bull again fool, this is not about you, but
about the process under observation

>
> Only in very limited contexts (when writing about complex
> numbers and complex functions), one can work with so called
> "multi-valued" functions and "principal values", i.o.w. with
> functions from C to the power set of C. In that special case
> one can write something like
> (-1)^(1/2) = { i, -i }

wrong moron, (-1)^(1/2) only gives i,
what a moron ...ahaha AHAHA ahaha...

>
> Dirk Vdm
>
>
>
> > Same way with the nature of a complex
> > number.
> >
> > This probably doesn't help, but I thought I'd give it a shot anyway.
> >
> > --
> > // The TimeLord says:
> > // Pogo 2.0 = We have met the aliens and they are us!

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