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**wcy****Member**- Registered: 2005-08-04
- Posts: 117

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 01:42:27)*

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

I've already discussed that on IRC and nobody could explain that too..

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**wcy****Member**- Registered: 2005-08-04
- Posts: 117

i suspect that it is illegal to square root both sides, since square rooting a negative number is not allowed

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,591

"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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 19,169

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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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