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)