The classical Maxwell system describing electromagnetic phenomena in an arbitrary inhomogeneous medium admits a representation in the form of a single biquaternionic equation [1]. In the talk some features and new applications of this representation, such as an explicit solution of the problem of a time-dependent one-dimensional electromagnetic wave propagation through an inhomogeneous medium [2] will be discussed. [1] V. V. Kravchenko, Applied quaternionic analysis. Research and Exposition in Mathematics Series, Vol. 28, Lemgo: Heldermann Verlag, 2003. [2] K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba Time-dependent one-dimensional electromagnetic wave propagation in inhomogeneous media: exact solution in terms of transmutations and Neumann series of Bessel functions. Lobachevskii Journal of Mathematics, v. 41, issue 5, 2020, 785–796.