Final answer:
The stage in the relationship life cycle where a leader and subordinate engage in formal interactions is the Stranger phase, which is characterized by professional and formal exchanges.
Step-by-step explanation:
In the relationship life cycle between a leader and a subordinate, the stage where they get to know each other through very formal interaction is known as the Stranger phase. During this phase, the interactions are typically characterized by formality and a reliance on professional roles as guidance for behavior and communication. As the relationship matures, interactions may become more personalized and informal, marking a transition into subsequent phases, like the Acquaintance phase or the Mature partnership phase. Understanding the dynamics of this relationship is important for achieving greater job satisfaction and growth opportunities.