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)