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Large Language Models (LLMs) have significantly advanced user-bot interactions, enabling more complex and coherent dialogues. However, the prevalent text-only modality might not fully exploit the potential for effective user engagement. This paper explores the impact of multi-modal interactions, which incorporate images and audio alongside text, on user engagement in chatbot conversations. We conduct a comprehensive analysis using a diverse set of chatbots and real-user interaction data, employing metrics such as retention rate and conversation length to evaluate user engagement. Our findings reveal a significant enhancement in user engagement with multi-modal interactions compared to text-only dialogues. Notably, the incorporation of a third modality significantly amplifies engagement beyond the benefits observed with just two modalities. These results suggest that multi-modal interactions optimize cognitive processing and facilitate richer information comprehension. This study underscores the importance of multi-modality in chatbot design, offering valuable insights for creating more engaging and immersive AI communication experiences and informing the broader AI community about the benefits of multi-modal interactions in enhancing user engagement.