Math Is Fun Forum

wcy

Member

Registered: 2005-08-04

Posts: 117

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 01:42:27)

wcy

Member

Registered: 2005-08-04

Posts: 117

Re: Paradox

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

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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 *

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,406

Re: Paradox

(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.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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