The remarkable fact is that the holistic mathematical interpretation of this important notion of the "imaginary" equates very closely with the conventional literary meaning.
So the imaginary in this (conventional) sense would imply the intervention of the unconscious in some phenomenal manner.
Indeed in a culture where what is "real" is so often equated with what can be consciously observed (in a direct sense), we often contrast what is "real" (conscious ) with what is "imaginary" (unconscious).
However because of the great lack of any developed holistic appreciation of mathematical symbols we are unable to make these significant links as between conventional and mathematical interpretation.
Again the remarkable implication of this is that that every mathematical symbol (or relationship) that can be defined in analytic terms, can be equally defined in a dynamic holistic manner and has direct relevance for both physical and psychological reality (which are complementary).
So the accepted belief that many relationships have a merely abstract mathematical meaning (without practical applications) is strictly speaking untenable.
Again the problem arises from the fact that we do not understand Mathematics in an integral fashion. Surprisingly therefore - despite its proven merits - a great deal of its potential relevance for understanding and structuring reality is completely overlooked.
For example the comprehensive number system is complex (with both real and imaginary aspects). However science for the most part, attempts to operate with solely real interpretations. Indeed the very word "reality" directly implies this bias. In other words despite all the problems posed for such an interpretation by quantum physics, predominantly for the scientific observer "reality" is what is real (i.e. consciously understood in a direct sense).
However the comprehensive number system is complex with both real and imaginary aspects.
Thus when we apply our basic axiom that every mathematical notion directly applies in dynamic terms to the physical and psychological domains, then this entails that these domains are complex in a holistic sense (with "real" and "imaginary" aspects).
As I have explained in psychological terms the "real" aspect applies to conscious meaning i.e. what can be consciously known (in a direct sense).
In complementary physical terms the "real" aspect applies to the "objective" products of such conscious knowledge.
In psychological terms the "imaginary" aspect applies to unconscious meaning that can be only known in an indirect conscious sense.
In physical terms the "imaginary" aspect applies to the (fundamental) dimensional ground of reality (empty space) that has a solely indirect and short-lived dynamic real identity (e.g. virtual particles).