  In previous papers we solved the Landau problems, indexed by 2M, for a
particle on the ``superflag'' S U (2|1)/[U (1) x U (1)], the M = 0 case being
equivalent to the Landau problem for a particle on the ``supersphere'' S U
(2|1)/[U (1|1)]. Here we solve these models in the planar limit. For M = 0 we
have a particle on the complex superplane C(1|1) ; its Hilbert space is the
tensor product of that of the Landau model with the 4-state space of a
``fermionic'' Landau model. Only the lowest level is ghost-free, but for M > 0
there are no ghosts in the first [2M ]+1 levels. When 2M is an integer, the
([2M ] + 1)th level states form short supermultiplets as a consequence of a
fermionic gauge invariance analogous to the ``kappa-symmetry'' of the
superparticle.
