However, the reciprocals of
and
are
and
, respectively, so that the implication
does not apply. In some situations, the sign of zero is a valuable bit of information, particularly in complex arithmetic where points on the real or imaginary axis (that is, with one zero component) are associated with the half-plane on one or the other side of the axis, according to the sign of the zero component.
Normally, you need take no extra care with the sign of zero. But when you evaluate functions with poles, like the rational function below, you must be aware of the behavior of zero in reciprocation. Here is a rational function with two poles.