  We study a two-dimensional electron gas in a perpendicular magnetic field in
the presence of both Rashba and Dresselhaus spin-orbit interactions. Using a
Bogoliubov transformation we are able to write an approximate formula for the
Landau levels, thanks to the simpler form of the resulting Hamiltonian. The
exact numerical calculation of the energy levels, is also made simpler by our
formulation. The approximate formula and the exact numerical results show
excellent agreement for typical semiconductors, especially at high magnetic
fields. We also show how effective Zeeman coupling is modified by spin-orbit
interactions.
