Objective: Understanding neural mechanisms underlying cognitive workload is crucial for advancing our knowledge of human cognition and mental processes. In this study, we utilized electroencephalography (EEG) analysis to investigate brain activity associated with varying mental cognitive workloads from a psychological perspective. Method: We employed a publicly accessible EEG dataset consisting of a cohort of 36 healthy volunteers (75% female), aged 18 to 26 years, while the participants were at rest or engaged in an arithmetic task to explore mental cognitive workload. After preprocessing to reduce noise and various artifacts and to obtain a clean signal for every subject, functional connectivity and complexity features were calculated from EEGs through the coherence and permutation entropy algorithms, respectively. Then, repeated measures analysis of variance (ANOVA) was conducted to assess the differences in complexity and connectivity measures across various brain regions between the rest and task states. Results: Brain sites showed significant within-subject effects, and the interaction between states and channels was significant for connectivity values (F = 3.68, P = 0.034). Post hoc comparisons indicated that FP1-F7, FP1-F8 and FP1-Fz connectivity were significantly lower during the task state compared to the rest state (P < 0.05). Moreover, F4-P3, F4-P4, FP1-O1, FP2-O2, F3-O1, F4-O1, F8-O1, C4-O1, F3-O2, F4-O2, F7-O2, F8-O2, Fz-O1, Fz-O2, Cz-O1 and Fz-P4 connectivity were significantly higher during the arithmetic task state (P < 0.05). Furthermore, brain sites showed significant within-subject effects and the interaction between states and channels was significant for entropy values (F = 3.50, P = 0.041). Post hoc comparisons indicated that the permutation entropy was significantly higher in the FP1, T3, T4, P4 and Pz channels during the arithmetic task compared to the rest state (P < 0.05). Conclusion: During arithmetic tasks, the increased connectivity in the frontoparietal and frontooccipital networks and heightened complexity in the prefrontal, temporal and parietal lobes reflect the collaborative engagement of brain areas specialized in numerical processing, attention, working memory, cognitive control, and visual-spatial cognition. These changes in connectivity and complexity facilitate the integration of multiple cognitive processes essential for effective arithmetic problem-solving.