--- In TekScopes@..., Lars Ahlstr?m <lea56@...> wrote:
Yeah, I understand. Its just to accept.
But the whole brain of mine want to give the result [ sqrt(-1) = -
1 ]
!!! =)
If I draw a carthesian coordinate system and pinpoint X=1 and Y=1 I
get a
square of the sides = 1.
The square is 1. meter, mm, inch, foot or whatever
Your square of area=1 in the first quadrant of the XY plane, this is
correct.
And if I pinpoint X= -1 and Y= -1 I get a square with the sides -1,
and the
area is then -1. foot, inch, yard or whatever.
The area of the square in the third quadrant is area=1 as well.
Remember that Area = length * height for a square, that being Area = -
1 *-1 = 1, Area is not negative unless it is of a hole or empty space.
The root of -9 is -3 !!! (I think¡;)
Almost. The root of -1 is "i" for math people, and is "j" for
electronics people.
i or j being root(-1)
i or j squared = -1,remember (root(-1))^2 the root and exponent cancel
i or j ^4th power = -1 *-1 = 1
you get the idea.
So, root(-9)= 3i or 3j for electronics people.
This ordinate in the complex plane is O= 0 + 3j, or simply 3 in the y
direction, and 0 in the x direction. There are lots of ways you can
play with this to give all kinds of phasors and vectors.
Matt
-----Ursprungligt meddelande-----
Fr?n: TekScopes@... [mailto:TekScopes@...]
F?r
arthurok
Skickat: den 30 december 2006 23:57
Till: tekscopes@...; Kuba Ober
?mne: Re: SV: [TekScopes] Invitation for another exchange of
questionably
useful information.
its a shared "delusion"
----- Original Message -----
From: Kuba Ober
To: tekscopes@yahoogrou <mailto:tekscopes%40yahoogroups.com> ps.com
Sent: Saturday, December 30, 2006 12:02 PM
Subject: Re: SV: [TekScopes] Invitation for another exchange of
questionably
useful information.
On Friday 29 December 2006 05:38, you wrote:
That post reminds me of my own high school drama: The j-omega
method.
The root of minus 1¡ still bugs me. Haven't yet figured it out
after 33
years...
For me it was too mind blowing. Had to stop thinking before I got
a
±è²õ²â³¦³ó´Ç²õ¾±²õ¡
And¡ our teacher back then, was a well known idiot, that (by the
rumour)
got a anonymously job advertise in his mail for this teacher job
from a
former headmaster. He was totally incompetent as a mathematician
teacher,
and had one item in his track record only: as a mechanical
instrument tech
at ASEA. He was totally unable to give me the idea (part from my
own
brains
lack of fantasy) of the "root of minus one".
Well, it's an abstract concept, I guess it's better treated like
one. Your
only "idea" should be of the properties of this number, and some
applications
that suit your interests.
I don't think I have any other "ideas" here. You can go pretty far
by just
knowing that the number has "otherwise" normal properties, i.e. you
treat it
like any other number that only doesn't "mix" (in addition) with
real
numbers. And when you square it, it goes away. I did my grad level
vibrations
course without using any other "higher" properties (whatever those
might be)
of sqrt(-1). I guess it shows what a powerful concept it is: only
minimal
properties are necessary to extract a lot of mathematical
expression power.
Cheers, Kuba
