[dayglored]

I think the error is in this step:

1 = (-1)²
1 = √(-1)²

While it is true that the square of 1 and the square of -1 are the same, that does not mean that 1 = -1

But your post is a neat challenge, and made me stop and think... thanks!

[PA Engineer]

While it is true that the square of 1 and the square of -1 are the same, that does not mean that 1 = -1

Absolutely. ;-)