Abstract: The complex vector expression of electromagnetic field is introduced on the base of Maxwell equations and Lorentz force equation, and apply them to formulae the electromagnetic field, including the foundation of the electromagnetic field in complex vector expression, law of conservation of charge, law of conservation of energy, vector potential and scalar potential, momentum, energy, tensor in electromagnetic field, relativistic covariance, and so on. Comparing with electrodynamics, some conclusions are stated.

Key words: electromagnetic field, Maxwell equations, law of conservation of charge, law of conservation of energy, Lorentz force, energy density, Poynting vector, momentum density, momentum flow density, relativistic covariance