First of all, all colors are imagined only in our minds.
Second, the term imaginary color already exists, and it refers to a specific thing [0], and the colors on the line of purple are not one of them. What you are describing is a non-spectral color. They exist in day to day life and in nature, they simply do not have an associated wavelength.
What exactly are you trying to prove? The gradient between red and blue (magentas) are the only fully saturated colors that we can perceive, which aren't part of the electromagnetic spectrum. That's fantastic. Do you want to waste your life arguing about nothing instead of enjoying the miracles of nature?
