Good communication is not just data transfer. You need to show people something that addresses their anxieties, that accepts their anger, that is credible in a very gut-level sense, and that evokes faith in the vision.
The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).