Granular events, instantiated in a document by predicates, can usually be grouped into more general events, called complex events. Together, they capture the major content of the document. Recent work grouped granular events by defining event regions, filtering out sentences that are irrelevant to the main content. However, this approach assumes that a given complex event is always described in consecutive sentences, which does not always hold in practice. In this paper, we introduce the task of complex event identification. We address this task as a pipeline, first predicting whether two granular events mentioned in the text belong to the same complex event, independently of their position in the text, and then using this to cluster them into complex events. Due to the difficulty of predicting whether two granular events belong to the same complex event in isolation, we propose a context-augmented representation learning approach CONTEXTRL that adds additional context to better model the pairwise relation between granular events. We show that our approach outperforms strong baselines on the complex event identification task and further present a promising case study exploring the effectiveness of using complex events as input for document-level argument extraction.