Final answer:
Sleep spindles and K-complexes are distinctive brain-wave activities indicating sleep, specifically during stage 2 of non-REM sleep.
Step-by-step explanation:
The distinctive bursts of brain-wave activity that indicate a person is asleep during stage 2 of non-REM sleep are called sleep spindles. These are rapid bursts of high-frequency brain waves that may play a role in learning and memory. Additionally, during this stage, we also observe the appearance of K-complexes, which are very high amplitude patterns of brain activity that might respond to environmental stimuli and serve as a bridge to higher levels of arousal.