  The supercomplexification is a special method of N=2 supersymmetrization of
the integrable equations in which the bosonic sector could be reduced to the
complex version of these equations. The N=2 supercomplex Korteweg de Vries,
Sawada-Kotera and Kaup-Kupershmidt equations are defined and investigated. The
common attribute of the supercomplex equations is appearance of the odd
hamiltonian structures and superfermionic conservation laws. The odd
bi-hamiltonian structure, Lax representation and superfermionic conserved
currents for new N=2 supersymmetric Korteweg de Vries equation and for
Sawada-Kotera, are given. The N=2 supercomplex Kaup-Kupershmidt equation is
defined for which the odd bi-hamiltonian structure is presented with its
superfermionic conserved currents.
