4 (Sqrt(-1))^2 = Sqrt(-1)*Sqrt(-1) Expand the defintion of i 5 (Sqrt(-1))^2 = Sqrt(-1 * -1) Rule: Sqrt(x)*Sqrt(y) = Sqrt(x*y)In algebra, there is a rule which states that the product of the square roots of two non-negative integers is the square root of their product. That is,
Sqrt(a) * Sqrt(b) = Sqrt(a*b)for non-negative a, b.
The key here is the word "non-negative." In line 4, the rule is applied to a=b=-1, which are certainly negative. The abuse of the rule allows the problem to conclude that i^2 equals 1, which is false (by definition).
Moral: the qualifiers in theorems are very important.