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We consider a phytoplankton-zooplankton interaction model which depends on two complementary nutrients. For a realistic representation in chemostat plankton ecosystem, we have incorporated various natural phenomena such as dissolved limiting nutrients with nutrient uptake functions and yield constants. For the model with two different constant nutrient inputs with same constant washout rate, existence and stability of non-negative equilibria as well as persistence are given. We analyze the behavior of solution of model in order to answer the biological question and seek to determine the limiting behavior of the surviving organisms and the nutrients. It is observed that the constant nutrient inputs of two complementary nutrients play an important role to change steady state behavior of the system. Further it is observed that if the dilution rate of chemostat crosses certain critical value, the system enters into Hopf-bifurcation. Finally, we have derived the explicit algorithm which determines the direction of Hopf-bifurcation. Computer simulations have been carried out to illustrate different analytical results. [ABSTRACT FROM AUTHOR]