Thread: 1 = -1?

I posted this "proof" in the 1/0 thread yesterday. I followed it up with discussion about another strange issue in math that I thought in some abstract way might be related, and then the discussion went in the direction of the second issue. So, I am starting a new thread to discuss the "proof" below. I do not know its resolution, other than that it is a reductio ad absurdum of imaginary numbers. I am open to other perspectives.

-1 = -1

1/-1 = -1/1

sqrt (1/-1) = sqrt (-1/1)

sqrt 1 / sqrt -1 = sqrt -1 / sqrt 1

1/i = i/1

i(1/i) = i(i/1)

1 = i^2

1 = -1


What is the deal with that?