No, it's impossible, even in principle, to answer that question. You can draw a picture for either answer.
"Left" and "right" are a dipole. Neither one can exist without the other, and they are symmetric. It's the same issue as we have with the conjugates discussed in Galois Theory.
In fact, in an algebraic (non-ordered/arithmetic/analytic) perspective, it's misleading to use the symbols + and - to label the conjugates in field extensions like sqrt2 and i. Left and Right are better names than + and - for those conjugate pairs. Only when we impose an arithmetic ordering (which is not needed in the theory of algebraic equalities) is it meaningful to use + and -: -sqrt(x) < 0 < +sqrt(x), where x is a positive real number.
(and when x is a negative real number, we immediately see the problem with - again: -i and i are not separable via ordering with respect to 0.)
"Left" and "right" are a dipole. Neither one can exist without the other, and they are symmetric. It's the same issue as we have with the conjugates discussed in Galois Theory.
In fact, in an algebraic (non-ordered/arithmetic/analytic) perspective, it's misleading to use the symbols + and - to label the conjugates in field extensions like sqrt2 and i. Left and Right are better names than + and - for those conjugate pairs. Only when we impose an arithmetic ordering (which is not needed in the theory of algebraic equalities) is it meaningful to use + and -: -sqrt(x) < 0 < +sqrt(x), where x is a positive real number.
(and when x is a negative real number, we immediately see the problem with - again: -i and i are not separable via ordering with respect to 0.)