Quote:
|
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.
|
Actually, square roots work
exactly the same for complex numbers. The problem is that squaring is not an invertable function and, thus, square root functions (note the plural) cannot be used to preserve equality.
So, in my esteemed opinion, the fallacy is the use of sqare roots...
PS. I'm sorry to bait the debate but I'm short on time at the moment. I'll clear this up, later...