RE: Dividing by variable when solving algebraic equation
October 30, 2016 at 11:48 pm
(This post was last modified: October 30, 2016 at 11:51 pm by mihoda.)
(October 27, 2016 at 3:05 am)Alex K Wrote: 1=sqrt(1)=sqrt(-1 * -1)=sqrt(-1)*sqrt(-1)= i*i=-1
The error is in the first equality.
sqrt(1) = +-1
When you later split the factors you are explicitly forcing one branch of the solution by again, reducing a choice:
sqrt(-1) = +-i
So in full:
+-1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = +-i * +-i = +-1
