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## #1 2005-08-07 23:41:47

wcy
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i²=-1

(-1/1)= (1/-1)
(i²/1)= (1/i²)
√(i²)/√1= (√1)/(√i²)
i/1= 1/i
i²= 1 (cross-multiplication)

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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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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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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"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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#### 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.