In this paper, optical effects of a hybrid complex system consisting of a semiconductor quantum dot and a metal nanoparticle interacting with a weak field is investigated. Nonlinear density matrix equations are used in order to describe optical properties of the quantum dot, the nanoparticle, and the entire system. Then, dependency of the susceptibilities of these component on the interparticle distance between the quantum dot and the nanoparticle is studied.  It is demonstrated that for a wide range of frequencies, susceptibility of the quantum dot leads to gain without inversion and is calculated that the susceptibility is severely dependent on presence of the metal nanoparticle