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# Squishy's sig... what the hell? watch

1. √(-1) = √(-1)
√(-1/1) = √(1/-1)
√(-1)/√(1) = √(1)/√(-1)
√(-1)√(-1) = √(1)√(1)
-1 = 1
Call me thick but i really dunno whats wrong with it..? Damn maths to hell
2. Square root isnt a valid function, √1 = + or -1
3. Square root isnt a valid function, √1 = + or -1
I disagree. √x means the positive square root of x only.

This is often confused with the correct statements : x^2 = 4 => x = +2 or -2 .

llduncanll:

Your third line, √(-1)/√(1) = √(1)/√(-1), is not a valid statement: i = 1/i is not true.

Why does it not follow logically from the second statement?

The distributive law for square roots only holds if a,b are positive real numbers i.e. √(a/b) = √a/√b only if a,b are positive real numbers
4. can you prove the distributive law is only true for positive real numbers?
5. Simple. Assume it is true for negative real numbers, see that leads to a contradiction. QED.
6. gosh that seems such a copout
7. How do you prove it holds for positive real numbers though?
8. we want to show root(a/b) = root(a)/root(b)

a/b = ab^-1

root(ab^-1) = a^.5b^-.5 = a^.5/b^.5

is that a proof?
9. oh yeah, good point guys i was just browsing around last night and all of a sudden it jumped out at me n slapped me round the face a few times... cheers for clearing it up!
10. Yup, the flaw in my sig is the jump from the second to the third line. Division by complex numbers is not the same as division by real numbers...didn't mean it to be confusing, it's just one of those warnings about generalising the properties of real numbers to all complex numbers.

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Updated: August 1, 2004
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