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i = -i ? Watch

1. I know it is not really a study help but i couldn't find any sort of maths debate part.

i = √-1 = √1/-1 = 1/i = i / i^2 = -i

What is going on, anyone?
(I think it might simply be a simple flaw rather like 1/0 is undefined in real numbers although I don't really think so.)
I would appreciate any opinions and especially a hardcore proof of some sort...
2. How do you go from i/i^2 to -i?

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3. (Original post by harribo12345)
How do you go from i/i^2 to -i?

Can't see the mistake myself, but I think the mistake has gotten be in the transition between , since the rest of it checks out.

Edit: a quick check on Wikipedia shows that the rule only applies to non-negative values of a and b, so there's the mistake.
4. The square root function is multivalued. Both i and -i give -1 when squared.

Perhaps writing the numbers in exponential form may give some insight:

Or

and are both valid ways of writing -1, but they given different results when the square root is taken.
5. (Original post by Kerch)
The square root function is multivalued. Both i and -i give -1 when squared.

Perhaps writing the numbers in exponential form may give some insight:

Or

and are both valid ways of writing -1, but they given different results when the square root is taken.
It's true that i and -i are algebraically the same (hence why when solving complex roots, the 'mirror' complex number is always a solution, also). However, they are quantitatively different: hence why the i = -i statement, in the form it is above, is false. This is easily seeable if you divide the equation by i and seeing what comes out.

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Updated: April 8, 2013
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