  We consider recovering analytically the (generally complex) parameters $\mu$,
$M_1$ and $M_2$ of the gaugino and Higgsino Lagrangian, from appropriate
physical input in the chargino and neutralino sectors. For given $\tan\beta$,
we obtain very simple analytic solutions for $M_2$, $| \mu|$, $Arg[\mu]$ in the
chargino sector and a twofold $| M_1 |$, $Arg[M_1]$ analytic solution in the
neutralino sector, assuming two chargino, two neutralino masses, and one of the
chargino mixing angles as physical input. The twofold ambiguity in the
neutralino parameters reconstruction may be essentially resolved by measuring
the $e^+e^- \to \chi^0_1 \chi^0_2$ production cross-section at future linear
collider energies, which we study explicitly with the phase dependences. Some
salient features and specific properties of this complex case gaugino "spectrum
inversion" are illustrated and compared with the similar inversion in the real
case. In particular, our algorithms exhibit in a direct and transparent way the
non-trivial theoretical correlation among the chargino and neutralino
parameters, and the resulting allowed domains when only a subset of the
required physical input masses and production cross-sections is known.

High Energy Physics - Phenomenology