Question

I may be missing something obvious here, but why is an expression such as sqrt-4 always simplified as 2i and not -2i?

Answer 1

for the same reason that √4 = 2 and not -2

even though both 2^2 and (-2)^2 are 4, the √4 is defined as 2.

So, √-4 = √4 √-1 = 2i

√-1 is defined as i, not -i, even though (-i)^2 = -1 as well.