Quote:
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Originally Posted by vinaur
You have some good reasoning there, however consider the following (I start wit step 5 from my previous post):
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
In this example you cannot get two answers for sqrt(-1) because you are not taking the sqrt. The mistake is somewhere else....
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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.