The square root function does not easily extend beyond the non-negative reals. There may be examples where what you did holds but for all complex numbers it would not. Also, when we say √ 4 we just mean +2, the principal square root, not the -2.
√( -1)*√( -1) = √[( -1)( -1)]
you are not allowed to do that with two complex numbers.
Read this http://math.stackexchange.com/questions … stribution
, especially Lee Mosher's answer.
That is the reason you are always told when working with a negative inside there to pull out a square root of -1 and to write is as i.