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Originally Posted by a-j
Good point.
The problem is going from sqrt(1/-1) to sqrt(1)/sqrt(-1)
1/i = -i, so in fact it should start out
5) sqrt(-1/1)=sqrt(1/-1)
6) sqrt(-1)/sqrt(1)=-sqrt(1)/sqrt(-1)
7) sqrt(-1)*sqrt(-1)=-sqrt(1)*sqrt(1)
8) sqrt(-1)^2=-sqrt(1)^2
9) -1=-1
The square root properties (sqrt(a/b) = sqrt(a)/sqrt(b)) don't exactly work the same for complex numbers.
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Good job! The problem is in fact in step 6.
Here's a different explanation for it though.
More classic falacies!!