Urban vitality is crucial for sustainability, contributing to social cohesion, information exchange, and overall quality of life. Understanding and quantifying urban vitality is essential for effective planning and policymaking, yet it remains a complex task. Previous studies have primarily focused on single-dimensional measures of urban vitality, overlooking the multifaceted nature emphasized by Jane Jacobs, including spatiotemporal dimensions. This study revisits Jacobs's urban vitality, focusing on three key indicators of intensity, diversity, and consistency of urban vitality. Additionally, we explore the relationships between urban complexity and urban vitality. We employ variety, uniformity, and connectivity metrics to assess urban complexity, which examines the physical structures of buildings, streets, and blocks. Linear regression and Maximal Information-based Nonparametric Exploration statistics for non-linearity analysis are used to determine the associations between urban complexity and urban vitality. Our findings reveal nuanced details of the relationships. Notably, variety and connectivity variables have more significant influences on urban vitality than those related to uniformity. Furthermore, the analysis highlights the differential impacts of complexity variables on different types of vitality. These insights provide valuable guidance for planners and policymakers, facilitating the design of sustainable and vibrant cities by considering optimal complexity measures of built environment that enhance urban vitality.