  Some new representations of the supersymmetric transformations are derived,
and the supermultiplets are introduced. Based on these representations, various
formulations (equations, commutation relations, propagators, Jacobi identities,
etc.) of bosons and fermions may be unified. On the one hand, the mathematical
characteristic of particles is proposed: bosons correspond to real number, and
fermions correspond to imaginary number, respectively. Such fermions of even
(or odd) number form bosons (or fermions), which is just consistent with a
relation between imaginary and real number. The imaginary number is only
included in the equations, forms, and matrixes of fermions. It is connected
with relativity. On the other hand, the unified forms of supersymmetry are also
connected with the statistics unifying Bose-Einstein and Fermi-Dirac
statistics, and with the possible violation of Pauli exclusion principle; and a
unified partition function is obtained. Therefore, one of the possible
developments is the higher dimensional complex space.
