Collisionless damping of plasma waves as a real physical phenomenon does not exist

Trivial logic of collisionless plasma waves is reduced usually to using non-linear complex exponentially damping/growing wave functions to obtain a complex dispersion equation for their wave number k1 and the decrement/increment k2 (for a given real frequency ω and complex wave number k ≡ k1-ik2 ), whose solutions are ghosts k1, k2 which do not have anything to do at k2 ≠0 with the solution of the real dispersion equation for the initial exponentially damping/growing real plasma waves with the physically observable quantities k1, k2 for which finding should be added, in this case, the second equation of the energy conservation law. Using a complex dispersion equation with non-linear complex wave functions for the simultaneous determination of k1 and k2 violates the law of energy conservation, leads to a number of contradictions, is logical error, and finally also the mathematical error leading to both erroneous statement on the possible existence of exponentially damping/growing harmonic wave solutions and to erroneous values k1 and k2. Mathematically correct conclusion about the damping/growing of virtual complex non-linear waves of collisionless plasma is wrongly attributed to the actual real plasma waves. A brief discussion is also on formalism of complex conductivity and dielectric permittivity with the ability to use their real values.