Proving the Equivalence of √(1) and √(-1)(-1)

[Yh Hoo]

1 = √(1)
= √(-1)(-1)
= (√-1)(√-1)
= i.i
= i^{2}
= -1
Is this a correct equation??
anythings wrong with this?
i think theoretically it is correct but it seems like
√(1) = √(-1)(-1)
√(1) = √(1)(1) also!
so how to explain this??

 

[DonAntonio]

1 = √(1)
= √(-1)(-1)
= (√-1)(√-1)
= i.i
= i^{2}
= -1
Is this a correct equation??
anythings wrong with this?
i think theoretically it is correct but it seems like
√(1) = √(-1)(-1)
√(1) = √(1)(1) also!
so how to explain this??

Squaring is a double branched complex variable function, and thus "usual" properties in real numbers can fail miserably.

In this case the problem appears in the third equality: it isn't true without imposing certain restrictive conditions.

DonAntonio