  This article is devoted to the spectral analysis of the electro-magnetic
Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we
derive a pseudo-differential effective operator that allows us to describe the
spectrum in various situations and appropriate regions of the complex plane.
Not only results of the selfadjoint case are proved (or recovered) in the
proposed unifying framework, but new results are established when the electric
potential is complex-valued. In such situations, when the non-selfadjointness
comes with its specific issues (lack of a "spectral theorem", resolvent
estimates), the analogue of the "low-lying eigenvalues" of the selfadjoint case
are still accurately described and the spectral gaps estimated.
