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Offline Munchor

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Imaginary Numbers Question
« on: February 09, 2011, 04:22:26 pm »
No, I'm not asking you to tell me how they work and general stuff.

But the other day my teacher said:

x²>0

And I thought... Hm, any number ² will be bigger than 0, since all squared numbers are positive. However, I just checked:

Code: [Select]
>>> 0**2
0
>>>

And it seems, 0² will be 0, so x²>=0.

What I want to know is if any imaginary number when squared will be minor than 0. Thanks.
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Offline AngelFish

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Re: Imaginary Numbers Question
« Reply #1 on: February 09, 2011, 04:25:23 pm »
Any purely imaginary number squared will be a negative number. X2>0 is only true for numbers along the real line. Along the imaginary line, numbers like i2 (which equals -1) are not necessarily greater than 0.
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∂²Ψ    -(2m(V(x)-E)Ψ
---  = -------------
∂x²        ℏ²Ψ

Offline ztrumpet

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Re: Imaginary Numbers Question
« Reply #2 on: February 09, 2011, 04:27:35 pm »
Well, the definition of i is "the square root of negative one", so if you did i2, you'd get -1.  Another example: 3i2=-3

You can check this on your calculator by hitting [mode] and changing to to a+bi. :)

Quote from: Scout on February 09, 2011, 04:22:26 pm
And it seems, 0² will be 0, so x²>=0.
Correct.  I believe what your teacher meant to say was "any non-zero number squared will be greater than zero." :D
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Offline Munchor

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Re: Imaginary Numbers Question
« Reply #3 on: February 09, 2011, 04:29:12 pm »
Quote from: Qwerty.55 on February 09, 2011, 04:25:23 pm
Any purely imaginary number squared will be a negative number. X2>0 is only true for numbers along the real line. Along the imaginary line, numbers like i2 (which equals -1) are not necessarily greater than 0.

Yes!
* Scout wins.

My teacher wrote this:

x²>0

I immediately shouted "x²>=0". And he said, "Oh thanks *myname*".

Then I said:

"x²>0,x IR"

And then he said "Well, that doesn't really matter".

But it seems it does. Thanks.
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Offline jnesselr

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Re: Imaginary Numbers Question
« Reply #4 on: February 09, 2011, 05:44:40 pm »
It does matter, but probably not as far as your class is concerned. ;-)
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Offline Juju

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Re: Imaginary Numbers Question
« Reply #5 on: February 09, 2011, 11:08:17 pm »
Yes, usually, teachers don't really want to mess with imaginary numbers unless they are actually teaching you imaginary numbers, so they would always say something like "x² ≥ 0 ∈ ℝ".
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Offline Munchor

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Re: Imaginary Numbers Question
« Reply #6 on: February 13, 2011, 10:19:36 am »
Quote from: juju2143 on February 09, 2011, 11:08:17 pm
Yes, usually, teachers don't really want to mess with imaginary numbers unless they are actually teaching you imaginary numbers, so they would always say something like "x² ≥ 0 ∈ ℝ".

Yeah, they just say that, but nobody really asks why it has to be in IR, at least in my class, they only care about maths for tests and grades, not maths as Maths :)
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Offline Happybobjr

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Re: Imaginary Numbers Question
« Reply #7 on: February 13, 2011, 10:45:17 am »
Quote from: Scout on February 09, 2011, 04:29:12 pm
I immediately shouted "x²>=0". And he said, "Oh thanks *scout".

we all know you're scout...:P
* Happybobjr wins
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Offline Munchor

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Re: Imaginary Numbers Question
« Reply #8 on: February 13, 2011, 10:47:40 am »
Quote from: Happybobjr on February 13, 2011, 10:45:17 am
Quote from: Scout on February 09, 2011, 04:29:12 pm
I immediately shouted "x²>=0". And he said, "Oh thanks *scout".

we all know you're scout...:P
* Happybobjr wins

But nobody here knows my real name xD
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Offline ztrumpet

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Re: Imaginary Numbers Question
« Reply #9 on: February 13, 2011, 10:58:56 am »
Quote from: Scout on February 13, 2011, 10:47:40 am
But nobody here knows my real name xD
Silly David...

* ZTrumpet can haz wins!!! O0
« Last Edit: February 13, 2011, 10:59:12 am by ztrumpet »
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Offline Munchor

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Re: Imaginary Numbers Question
« Reply #10 on: February 13, 2011, 12:19:00 pm »
Quote from: ztrumpet on February 13, 2011, 10:58:56 am
Quote from: Scout on February 13, 2011, 10:47:40 am
But nobody here knows my real name xD
Silly David...

* ZTrumpet can haz wins!!! O0

?? Sorry, I don't understand you. My real name isn't David Gomes xD

Or is it?
« Last Edit: February 13, 2011, 12:19:21 pm by Scout »
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Offline ruler501

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Re: Imaginary Numbers Question
« Reply #11 on: February 22, 2011, 09:15:44 pm »
I have one question i figured I should just add in here.
Can imaginary numbers be prime? I don't think negative numbers could be prime but I don't know about imaginaries. any help would be appreciated.
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Offline Xeda112358

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Re: Imaginary Numbers Question
« Reply #12 on: February 22, 2011, 09:16:56 pm »
I think prime numbers are described as natural numbers, so they must be integers >0
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Offline ruler501

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Re: Imaginary Numbers Question
« Reply #13 on: February 22, 2011, 09:26:10 pm »
OK thanks for the help I thought that would be the answer
(I'm so happy I'm not completely stupid :D)
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Offline Xeda112358

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Re: Imaginary Numbers Question
« Reply #14 on: February 22, 2011, 09:32:47 pm »
I feel happy that I actually understand what I just typed.
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