u/AlbuStark

Using completely regular rules of algebra, I can arrive at two different answers:

sqrt((-1)^2) = sqrt(1) = 1

sqrt((-1)^2) = sqrt((-1)(-1)) = sqrt(-1)sqrt(-1) = i*i = -1

Are both these answers valid? ChatGPT told me that distributing exponents for negative bases isn't allowed, which I've never heard of. Can someone explain why that is the case? Is it just so that this ambiguity doesn't happen?

I thought that expressing -1 as e^(i*pi) would clear things up, but I could still get two different answers depending on the order in which I evaluate it. Is there some background stuff happening with different branches that would make this a lot more intuitive?

Any help would be appreciated.