  In this paper we study the asymptotic behavior of a quadratic Schr\"{o}dinger
equation with electromagnetic potentials. We prove that small solutions
scatter. The proof builds on earlier work of the author for quadratic NLS with
a non magnetic potential. The main novelty is the use of various smoothing
estimates for the linear Schr\"{o}dinger flow in place of boundedness of wave
operators to deal with the loss of derivative. As a byproduct of the proof we
obtain boundedness of the wave operator of the linear electromagnetic
Schr\"{o}dinger equation on an $L^2$ weighted space for small potentials, as
well as a dispersive estimate for the corresponding flow.
