Spectral slope and neural complexity are affected in many neurophysiological disorders such as ADHD, autism or epilepsy and are modulated by sleep, anesthesia, and aging. Yet, the relationship between these two parameters remains unclear. Here, we evaluated the effects of sleep stage and task demands on spectral slope and neural complexity within a narrow- (30 - 45Hz) and broadband (3 - 45Hz) frequency range in 28 healthy male adults (21.54 ± 1.90 years) over three consecutive recordings with a set of different tasks (resting, attention and memory). We show that the slope steepens, and complexity decreases from wakefulness to N3 sleep. Importantly, slope and complexity are not only modulated by sleep but also differ between tasks, with flatter slopes and higher complexity being associated with more demanding tasks. While the slope and complexity are strongly correlated within 3 - 45Hz, we observe a functional dissociation in the 30 - 45Hz range. Critically, only the narrowband slope is steepest during REM sleep and associated with better task performance, especially in a Go/Nogo task. Our results demonstrate that both markers are powerful indices of sleep depth, task demand and cognitive performance. However, depending on the frequency range, they provide distinct information about the underlying brain state.