Wait, this is bugging me. sqrt(a*b) = sqrt(a) * sqrt(b) iff a,b are non-negative reals. So the third equality doesn’t hold.deep
There isn’t much about my world that makes sense right now, so I’m going to have to insist that basic algebra continues to work.The sqrt of (-1)(-1) is the sqrt of 1 which is 1.
However, you have to “pull out your eyes” as I told my students before you perform actions with the next grouping.
sqrt (-1) has to be rewritten as sqrt(-1)(1) which is i sqrt 1, which is i(1), which equals i
i times i does equal i squared which equals -1.
However, it is incorrect to state (sqrt -1)(sqrt -1) and work with it before pulling out the imaginary component. Sqrt (-1)(-1) is not the same thing as you have written by breaking it up. Imaginary numbers don’t work that way. You can only use properties of real numbers after you have removed the sqrt(-1) part, which is i.
That’s why 1 does not equal -1
(I was too tired and lazy to pull up Word and use correct symbols. Sorry, as it’s confusing to look at this way.)
that’s a lot of squirts.




