Task complexity and communication modes are two task design and implementation factors that have been found to affect second language (L2) learners' oral performance. While increasing task complexity and developing tasks according to the features of face-to-face and computer-mediated communication modes can optimise L2 production, few studies attend to how the two factors affect learner engagement in task performance--a crucial but under-explored concept contributing to academic achievement. To address this gap, this experimental study investigated the impact of task complexity (operationalised as ± pre-task planning time and ± intentional reasoning demand) and communication modes (synchronous video-based computer-mediated communication, SvCMC versus face-to-face real-time communication, FTF) on L2 learners' engagement in interactive oral tasks. Sixty-four English-as-a-second-language (ESL) learners formed their self-initiated dyads to perform three interactive oral tasks (from simple to + complex and ++complex conditions) on Zoom or in a physical classroom. They were also interviewed about their affective responses to the tasks. The oral discourse of task performance and interview data were analysed in terms of behavioural, cognitive, emotional, and social engagement. The findings revealed that task complexity affected the behavioural and cognitive engagement of FTF and SvCMC learners. SvCMC learners were behaviourally more engaged in task performance than their FTF peers, but mixed results were found in cognitive engagement. Mixed affective responses were reported by FTF and SvCMC learners for all task conditions. The findings suggest that increasing task complexity may partially engage L2 learners, and teachers need to consider the affordances of the two communication modes when designing tasks to engage learners in L2 production.