This article explores human-AI interaction with large language models or conversational agents in complex information tasks with a focus on prompt engineering strategies. The paper reviews the current literature on the use of artificial intelligence (AI) for complex information tasks that are often nonlinear and entail interpretation, organization, and synthesis of information. Building on the role prompting plays in enhancing generative AI responses, the study frames prompt engineering as a medium with the potential to enable users to iteratively tackle complex information tasks. It provides recommendations for the use of key prompting strategies such as task decomposition, iterative refinement, identification of audience and context, and role/persona assignment. Considering the notable importance of prompting as a critical AI literacy, the paper ends with several implications that might be conducive to enhance the human-AI communication in generative AI context.