As far as I know, every numerical field has a correspondence to reality - e.g. the natural numbers can be represented by counting apples (1, 2, 3 apples), and even the irrational numbers correspond to phenomena we find in nature (the ratios that pi and phi represent correspond to real phenomena).
But what would the imaginary numbers correspond to in nature? Can we find any phenomena that represents them? I'd like to distinguish between the complex numbers that unities the imaginary part with a real part, thus perhaps providing it a real correspondence, e.g. in certain representations of QM (although perhaps even complex numbers are problematic in this sense). A complex number, represented as the combination of the real part (a number from the ℝ field) and an imaginary part (i). My emphasis is on the numbers that appear in the imaginary part (the so-called "imaginary numbers", square root of -1).
Furthermore, if these kind of numbers cannot be represented in nature, does it mean they have an expiration date in our usage of them outside of math? Are they simply place-holders for the next mathematical discovery that does correspond to nature and that would replace them? (i.e. isn't it an aspiration of the natural sciences to prefer correspondence to nature?)