OT: mathematical conundrum

Ok, let's try this:
If 'i' is the square root of minus 1, what is 'i' squared?
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On Sun, 22 Nov 2015 11:50:10 -0000 (UTC), Cursitor Doom

-1
--

Chris

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On Sun, 22 Nov 2015 11:56:08 +0000, Chris Hogg wrote:

Bugger. You got it right straight away. I was hoping for a lengthy, argumentative thread on this!
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On Sun, 22 Nov 2015 12:03:47 +0000, Cursitor Doom wrote:

Anyway, it's j really.
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that depends on whether you are a mathematicial or an engineer. The latter tend to use "i" for current.
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Bob Eager wrote:

I thought the whole point about "i" was that it ain't real.
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On 22/11/15 12:14, Robin wrote:

http://mathforum.org/library/drmath/view/52613.html
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On Sun, 22 Nov 2015 12:14:03 +0000, Robin wrote:

Actually, it is. The label "imaginary numbers" is a misnomer.
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Cursitor Doom wrote:

If you say so. But I'll leave you to correct all the sources which talk about the way imaginary numbers extend the system of real numbers to give the complex number system. I was never more than a wannabe practical physicist so I've always deferred to mathematicians when it come to things like that.
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On 22/11/15 16:19, Robin wrote:

The idea is that complex numbers are essentially two dimensional whereas ordinary numbers are not.
So they can represent things that have orthogonal components, like amplitude and phase in voltages/currents etc.
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The Natural Philosopher wrote:

Thanks for that, although believe it or not, I do still recall a *few* things from O-level. That said, the use of complex numbers for probability amplitudes is about all I can now recall from Rudolf Peierls' lectures on quantum electrodynamics :(
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On 22/11/2015 12:19, Cursitor Doom wrote:

Indeed - partly a result of the early discoverers of them not really understanding that complex numbers were "real" and not just a mathematical slight of hand.
I find it easier to think of in two dimensions, where the real number line, is just a straight line where there is 0 deviation into the complex dimension.
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Whether it is or not, its square is still -1.
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On 22/11/2015 13:20, Tim Streater wrote:

Isn't that a bit like say: Pegasus without his wings is just an ordinary horse. It requires that Pegasus is there in the first place, surely?
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wrote:

This thread was entitled "mathematical conundrum". I've yet to understand what the conundrum is, perhaps I missed it, if so could someone point it out?
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On 22/11/2015 15:59, Tim Streater wrote:

I was puzzled what the conundrum was supposed to be, too.
Cursitor said (3rd post on this thread) "Bugger. You got it right straight away. I was hoping for a lengthy, argumentative thread on this!"
So, argue!
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On Sunday, 22 November 2015 12:13:57 UTC, Robin wrote:

It's a system for manipulating vectors. The i or j is at right angles to the normal.
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Since when? I've always known it as 'i'. See also https://en.wikipedia.org/wiki/Imaginary_number
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On Sun, 22 Nov 2015 12:48:57 +0000, Chris Hogg wrote:

i is j; they're the same thing. It's just that i already reserved in electronics and electrical engineering as the symbol for current, so in these disciplines we use j instead of i to avoid confusion.
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On 13:34 22 Nov 2015, Cursitor Doom wrote:

What's coming up next? Fourier transforms maybe. It's all too complex ;-)
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