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#1 2005-08-07 23:41:47
- wcy
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Paradox
i²=-1
(-1/1)= (1/-1)
(i²/1)= (1/i²)
√(i²)/√1= (√1)/(√i²)
i/1= 1/i
i²= 1 (cross-multiplication)
Contradiction!!
How to solve this paradox?
I also don't know the answer.
Last edited by wcy (2005-08-07 23:42:27)
#2 2005-08-08 00:02:35
- kylekatarn
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Re: Paradox
I've already discussed that on IRC and nobody could explain that too..
#3 2005-08-08 00:13:32
- wcy
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Re: Paradox
i suspect that it is illegal to square root both sides, since square rooting a negative number is not allowed
#4 2005-08-08 07:47:29
- MathsIsFun
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Re: Paradox
"How wonderful that we have met with a paradox. Now we have some hope of making progress." - Niels Bohr
I suspect it is this curious phenomenon:
(-1)² = 1²
-1 = 1 ...?
Making:
√(i²)/√1= (√1)/(√i²)
i/1 = 1/i ...?
Because:
1/i = (1 x i) / (i x i) = i/i² = i / -1 = -i
* basks in glow of very rare victory, hoping it lasts *
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#5 2005-08-08 14:39:12
- ganesh
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Re: Paradox
wcy wrote:
(i²/1)= (1/i²)
√(i²)/√1= (√1)/(√i²)
Normally, in such paradoxes, this is where the mistake lies.
Since a² = b²,
it cannot be inferred that a=b.
Taking square root on both sides of an equation should always have the
'±' sign, after the square root is worked out.
Character is who you are when no one is looking.