  The electronic properties of monolayer phosphorene are exotic due to its
puckered structure and large intrinsic direct band gap. We derive and discuss
its band structure in the presence of a perpendicular magnetic field. Further,
we evaluate the magneto-optical Hall and longitudinal optical conductivities,
as functions of temperature, magnetic field, and Fermi energy, and show that
they are strongly influenced by the magnetic field. The imaginary part of the
former and the real part of the latter exhibit regular {\it interband}
oscillations as functions of the frequency $\omega$ in the range
$\hslash\omega\sim 1.5-2$ eV. Strong {\it intraband} responses in the latter
and week ones in the former occur at much lower frequencies. The
magneto-optical response can be tuned in the microwave-to-terahertz and visible
frequency ranges in contrast with a conventional two-dimensional electron gas
or graphene in which the response is limited to the terahertz regime. This
ability to isolate carriers in an anisotropic structure may make phosphorene a
promising candidate for new optical devices.
