This paper provides an in-depth analysis of Wave Network, a novel token representation method derived from the Wave Network, designed to capture both global and local semantics of input text through wave-inspired complex vectors. In complex vector token representation, each token is represented with a magnitude component, capturing the global semantics of the entire input text, and a phase component, encoding the relationships between individual tokens and the global semantics. Building on prior research that demonstrated the effectiveness of wave-like operations, such as interference and modulation, during forward propagation, this study investigates the convergence behavior, backpropagation characteristics, and embedding independence within the Token2Wave framework. A detailed computational complexity analysis shows that Token2Wave can significantly reduce video memory usage and training time compared to BERT. Gradient comparisons for the [CLS] token, total input text, and classifier parameters further highlight Token2Wave's unique characteristics. This research offers new insights into wave-based token representations, demonstrating their potential to enable efficient and computationally friendly language model architectures.