This fake proof uses complex numbers to pull the wool over your eyes.

-1 1
--- = ---
1 -1

*(both sides are -1).*
sqrt(-1/1) = sqrt(1/-1)

*(apply the same operation to both sides)*
sqrt(-1) sqrt(1)
-------- = --------
sqrt(1) sqrt(-1)

*(square root of the quotient is quotient of square roots)*
-1 = 1

*(multiply by denominators)*