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vuurrobin
Advanced Member
Joined: 09 Aug 2006
Posts: 428
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 Posted: 21 Apr 2008 09:36:27 am Post subject: |
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someone at school gave me this, and I can't find whats wrong with it. can someone help me :confused: .
√(-1) = i
i² = -1
i²*i² = 1
i^4 = 1
i = 4√(1) or - 4√(1)
i = 1 or -1
i² = 1 or 1
-1 = 1 |
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magicdanw
pcGuru()
Calc Guru
Joined: 14 Feb 2007
Posts: 1110
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| Posted: 21 Apr 2008 10:25:42 am Post subject: |
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You mean, -1 doesn't equal 1? a, that explains all those failed math exams...  |
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Igrek
Member
Joined: 23 Aug 2007
Posts: 151
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| Posted: 21 Apr 2008 10:34:40 am Post subject: |
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i^4 = 1
i = 4√(1) or - 4√(1)
The mistake is here, how does he legitimate this step. |
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emperorwiggy
Newbie
Joined: 27 Mar 2008
Posts: 27
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| Posted: 21 Apr 2008 10:35:42 am Post subject: |
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This reminds me off the 1+1=1 therom. I have a t-shirt with it, but that's irrelevant.
I've never seen this before, otherwise, I would already know where the logic error is. I think that the transition from line 4 to line 5 - taking the fourth root - is wrong, but I don't remeber why. Perhaps I should start listening to my math teacher instead of playing games. |
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DarkerLine
ceci n'est pas une |
Super Elite (Last Title)
Joined: 04 Nov 2003
Posts: 8328
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| Posted: 21 Apr 2008 10:37:31 am Post subject: |
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x^4=1 is a fourth-degree polynomial equation, so when you're dealing with complex numbers it has 4 solutions (namely, 1, -1, i, and -i). Instead of saying i=1 or i=-1, the conclusion should be i=1, i=-1, i=i, or i=-i, and then i^2=1 or i^2=-1. No contradiction there.
Last edited by Guest on 21 Apr 2008 10:44:45 am; edited 1 time in total |
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vuurrobin
Advanced Member
Joined: 09 Aug 2006
Posts: 428
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| Posted: 21 Apr 2008 04:03:56 pm Post subject: |
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Quote: i^2=1 or i^2=-1
but then you have i²=1=-1, which is wrong, or am I wrong :confused:
complex numbers are confusing  |
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DarkerLine
ceci n'est pas une |
Super Elite (Last Title)
Joined: 04 Nov 2003
Posts: 8328
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| Posted: 21 Apr 2008 04:22:37 pm Post subject: |
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vuurrobin wrote: Quote: i^2=1 or i^2=-1
but then you have i²=1=-1, which is wrong, or am I wrong :confused:
complex numbers are confusing
[post="122682"]<{POST_SNAPBACK}>[/post]
It's i^2=1 or i^2=-1. What we've proved is that one of the two is true. In fact, it's always the case that i^2=-1, but that's stronger than what ends up proved.
It's true that "2+2=4 or 2+2=5." But you can't conclude from this that 4=5.
Last edited by Guest on 21 Apr 2008 04:23:11 pm; edited 1 time in total |
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bfr
Member
Joined: 13 Feb 2006
Posts: 108
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| Posted: 21 Apr 2008 09:25:24 pm Post subject: |
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It's just that the square root is defined as a function...it only gives one of the results. If it didn't, one of the square roots of 1 would be -1, and one of the fourth roots of 1 would be i, and things could work out. It's just taking advantage of the definitions of things. Maybe.
Last edited by Guest on 21 Apr 2008 09:30:47 pm; edited 1 time in total |
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vuurrobin
Advanced Member
Joined: 09 Aug 2006
Posts: 428
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| Posted: 22 Apr 2008 01:14:07 pm Post subject: |
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now I get it
thanks you guys  |
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