By the same token, any number times itself is non-negative.  i breaks existing rules too.  (lol)

You know, I could just have said, oh, since you're multiplying i times i the result is negative, by definition, and accepted that it works.  I could just be the kid who writes down what the teacher says and memorizes it for the test, instead of asking questions.  I suspect there is something else at work for the result to be correct, because the only reason given for using i was to represent the vertical axis.  At no point was there actually a quantity of -1, for which we found the root before multiplying by the second part of the complex number.

 

 

-Chuckk

 

 

On 11/11/05, Martin Peach <martinrp@vax2.concordia.ca> wrote:

Chuckk Hubbard wrote:

> What I'm getting at is that expressing rotation as complex numbers is
> no different than using cartesian coordinates.  Why, when you multiply
> two points, would one of the multiples turn negative?
> I see no reason you couldn't say i = 1/0.  Then 4*0*i=4.  That makes
> as much sense.

<OT lecture_and_rant>
Not really. Any number multiplied by zero becomes zero. You can't break
the existing rules. There is a philosophical need for i because
intuitively every number ought to have a square root, even negative
numbers. The other philosophical need comes from the idea that the
energy of an oscillator should be constant if the oscillator is at a
constant amplitude and frequency, but the observable output of the
oscillator passes through zero, which implies there is no energy there.
Where is the energy? In an imaginary dimension...imaginary just means
unobservable. This is basically how in quantum mechanics one decides
what is actually observable versus just virtual, so there is some
connection with reality here, but it's probably hard to grasp since
humans have never used such concepts until about a hundred years ago
simply because there was no practical use for them.
It also took a long time for people in Europe to accept the concept of
zero after it had been invented in North Africa and Central America and
elsewhere...in Roman numbers (I, II, III, IV...) there is no zero but in
Arabic numbers (0,1,2,3,) there is. The Maya used a shell glyph for zero
and dots and bars for the other numbers. I wouldn't get hung up on the
use of i, it's like using an empty shell for zero, a kind of handle on a
concept. Some people think that concepts cannot be expressed in a
language that doesn't already have words for them, but they are wrong.
The concepts are just expressed in a crooked, crooked way.
</OT lecture_and_rant>

Martin