Why does the result only equal the principal root? For example, why is the square root of -16 just 4i, instead of positive and negative 4i?
When I think about this, I see sqrt -16 as sqrt 16 * sqrt -1. The sqrt 16 is positive and negative 4 and square root -1 is i, I get the result pos and neg 4i. All my textbooks just list 4i. Why is that?
Forgive my syntax, but when the question is stated: simplify sqrt -16, I still believe the answer is + and - 4i. Yet, my texts show only 4i and do not include -4i. Is this simply for convention sake? Or a higher reason than I am missing? The solutions that I have seen thus far indicate, that it is convention, rather than pure mathematics that this is so.
Speaking with colleagues, I have been told that unless a positive/negative symbol is placed before the square root of -16 the expression can only be equivalent to 4i. Is this accurate? And if so, why?