In this paper, the complex involutive systems associated with the Ablowitz, Kaup, Newell, and Segur (AKNS) evolution equations are discussed. By means of the complex representations of the standard symplectic form and the standard Poisson bracket on the real space R2n, using the equivalent relations between the Hamiltonian canonical equations, it is proved that the complex involutive systems are exactly finite-dimensional completely integrable systems in the Liouville sense. Therefore, by mapping nonlinearly from the involutive solutions of the compatible Hamiltonian canonical equations to the AKNS evolution equations, the representations of the solutions of the AKNS evolution equations are obtained.