  Within the framework of the hypothesis offered by authors about
complex-valued nature of physical quantities, the effect of the Landau damping
has been explored with assumption that not only frequency can be a small
imaginary component but also a wave vector. The numerical solution of the
obtained dispersion equation testifies that uncollisional damping is
accompanied in a certain region of space by antidumping of waves, and in
particular situations antidumping may prevail over damping. It is possible that
this effect may explain the experimental difficulties connected with inhibition
of instabilities of plasma in the problem of controllable thermonuclear fusion.
