  The complex form of Maxwell equations has been constructed as one equation
for 3-dimensional complex A-vector. The real and imaginary parts of this vector
are described with use of electric and magnetic tensions accordingly. With
using a theory of generalized functions for new equations, the strong shock
electro-magnetic waves with the gap of tensions on fronts are considered. The
conditions on wave fronts have been received. It's shown that gap of the
tensions is tangent to the front of a wave, i.e. shock electromagnetic waves
are transverse and charges on the front of wave are absent. Generalized laws of
conservation of energy and charges have been received including ones on the
fronts of shock waves. The generalized solutions of this equations and solution
of Caushy problem have been constructed and the theorems of their uniqueness
have been proved including the shock waves.
