  Some aspects of the development of physics and the mathematics set one think
about relation between complex numbers and reality around us. If number to spot
as the relation of two quantities, from the fact of existence of complex
numbers and accepted definition of number it is necessary necessity complex
value to assign to all physical quantities. The basic property of quantity to
be it is more or less, therefore field of complex quantities, if it exists, it
is necessary is ranked.
  The hypothesis was proposed that lexicographic ordering may be applied to the
complex physical quantities. A set of the ranked complex numbers is quite
natural to arrange on a straight line that represents in this case a
non-Archimedean complex numerical axis. All physical quantities are located on
the relevant non-Archimedean complex numerical axes, forming a new reality -
"complex-valued" world.
  Thus, we get the conclusion that the resulting non-Archimedean complex
numerical axis may serve as an example of the ideal mathematical object -
hyperreal numerical axis. So, differentiation and integration on the
non-Archimedean complex numerical axis can be realized using methods of
nonstandard analysis.
  Certain properties of a new "complex-valued" reality, its connection with our
"real" world and possibility of experimental detection of complex physical
quantities are discussed.
