In this paper,we derive the Lindblad and Redfield forms of the master equation based on the Born-Markov master equation with and without the secular approximation for open multi-level quantum systems.The coefficients of the equations are re-evaluated according to the scheme in[(2019),Phys.Rev.A 99,022118].They are complex numbers rather than the real numbers obtained from traditional simplified methods.The dynamics of two models (one is an open three-level quantum system model,and the other is the model of phycoerythrin 545 (PE545) in a photosynthesis system) are studied.It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments,but a large distortion of the dynamics in others.These effects are discussed and characterized by studying the dynamics of nontdvial instances of multi-level systems in the presence of dissipation.