The vibrations of gyroscopic continua may induce complex mode functions. The continuous model governed by partial differential equations (PDEs) as well as the discretized model governed by ordinary differential equations (ODEs) are used in the dynamical study of the gyroscopic continua. The invariant manifold method is employed to derive the complex mode functions of the discretized models, which are compared to the mode functions derived from the continuous model. It is found that the complex mode functions constituted by trial functions of the discretized system yield good agreement with that derived by the continuous system. On the other hand, the modal analysis of discretized system demonstrates the phase difference among the general coordinates presented by trial functions, which reveals the physical explanation of the complex modes.