  In this paper a new look on the electro-magnetic duality is presented and
appropriately exploited. The duality analysis in the nonrelativistic and
relativistic formulations is shown to lead to the idea the mathematical model
field to be a differential form valued in the 2-dimensional vector space ${\cal
R}^2$. A full ${\cal R}^2$ covariance is achieved through introducing
explicitly the canonical complex structure ${\cal I}$ of ${\cal R}^2$ in the
nonrelativistic equations. The connection of the relativistic Hodge * with
${\cal I}$ is shown and a complete coordinate free relativistic form of the
equations and the conservative quantities is obtained. The duality symmetry is
interpreted as invariance of the conservative quantities and conservation
equations.
