When working with complex data paths in Splunk SOAR, particularly within playbooks, the dot (.) operator is used to access sub-elements within a larger data structure. This operator allows for the navigation through nested data, such as dictionaries or objects within JSON responses, enabling playbook actions and decision blocks to reference specific pieces of data within the artifacts or action results. This capability is crucial for extracting and manipulating relevant information from complex data sets during incident analysis and response automation.