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This paper proposes a complex boundary wave superposition method with a unique solution of full wavenumber based on the similarity between the acoustic wave superposition method (WSM) and the external excitation response of dynamic systems and combined with the idea that a damping system has a unique solution in dynamic theory. By placing the virtual equivalent source on the virtual boundary of complex space, the conventional WSM acquires damping properties comparable to those of the dynamical system. This approach successfully addresses the non-uniqueness of the solution at the eigenfrequency and is more efficient than the conventional combined layer potential method. The paper presents a comprehensive description of the proposed method, with a focus on theory, modeling, and parameter selection. The effectiveness of this method is evaluated by applying it to two types of acoustic problems, namely, radiation and scattering. The numerical results indicate that this method effectively addresses the non-unique problems encountered in conventional WSM. Furthermore, the proposed method is as accurate and efficient as the conventional WSM. [ABSTRACT FROM AUTHOR]