  In this paper, we are concerned with the inverse electromagnetic scattering
problem of recovering a complex scatterer by the corresponding electric
far-field data. The complex scatterer consists of an inhomogeneous medium and a
possibly embedded perfectly electric conducting (PEC) obstacle. The far-field
data are collected corresponding to incident plane waves with a fixed incident
direction and a fixed polarisation, but frequencies from an open interval. It
is shown that the embedded obstacle can be uniquely recovered by the
aforementioned far-field data, independent of the surrounding medium.
Furthermore, if the surrounding medium is piecewise homogeneous, then the
medium can be recovered as well. Those unique recovery results are new to the
literature. Our argument is based on low-frequency expansions of the
electromagnetic fields and certain harmonic analysis techniques.
