complex Maxwell-fields

Maxwell’s equation can be written in an unusual form in terms of the complex field \(\vec{X} = \vec{E}+\mathrm{i}\vec{B}\), with the two relations \(\mathrm{div}\vec{X} = 4\pi\rho\) and \(\mathrm{rot}\vec{X}-\mathrm{i}\partial_{ct}\vec{X} = 4\pi\mathrm{i}\jmath/c\). Can you introduce magnetic charges in a consistent way using this formalism?