Leibniz, G. Wilhelm (1646-1716) said that "complex numbers are a fine and wonderful refuge of the divine spirit, as if it were an amphibian of existence and non-existence." In science, imaginary numbers were and still are the great mystery. This fact leads to serious consequences in some cases. In particular, in order to get rid of the imaginary part, Born in 1926 proposed the well-known probabilistic interpretation of the complex wave Ψ-function. Since then, quantum mechanics (QM) loudly asserts that the physical sense has only the modulus squared of Schrödinger's wave function
This step caused a series of problems at the description of energetic structure (spectra) of atoms and gave rise to quantum electrodynamics (QED), which all time struggles against infinities. The QM formalism is also unable to describe directly the spatial structure of atomic spaces, etc.