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Helpful info on what a K complex is:

Neurophysiology
K-complex consists of a brief negative high-voltage peak, usually greater than 100 µV, followed by a slower positive complex around 350 and 550 ms and at 900 ms a final negative peak. K-complexes occur roughly every 1.0–1.7 minutes and are often followed by bursts of sleep spindles. They occur spontaneously[1] but also occur in response to external stimuli such as sounds, touches on the skin[3] and internal ones such as inspiratory interruptions.[4] They are generated in widespread cortical locations[1] though they tend to predominate over the frontal parts of the brain.[5]

Both K-complex and delta wave activity in stage 2 sleep create slow-wave (0.8 Hz) and delta (1.6–4.0 Hz) oscillations. However, their topographical distribution is different, and the delta power of K-complexes is higher.[6]

They are created by the occurrence in widespread cortical areas of outward dendritic currents from the middle (III) to the upper (I) layers of the cerebral cortex. This is accompanied by a decrease in broadband EEG power including gamma wave activity. This produces "down-states" of neuronal silence in which neural network activity is reduced.[1] The activity of K-complexes is transferred to the thalamus where it synchronizes the thalamocortical network during sleep, producing sleep oscillations such as spindles and delta waves.[7] It has been observed that they are indeed identical in the "laminar distributions of transmembrane currents" to the slow waves of slow-wave sleep.[1]

K-complexes have been suggested both to protect sleep and also to engage in information processing, as they are both an essential part of the synchronization of NREM sleep, while they also respond to both internal and external stimuli in a reactive manner.[8] This would be consistent with a function in suppressing cortical arousal in response to stimuli that the brain needs to initially process in regard to whether it is dangerous or not.[1]

Another suggested function is aiding the activation homeostasis of synapses[9] and memory consolidation. The activation thresholds of cortical synapses become lowered during wakefulness as they process information, making them more responsive, and so need to be adjusted back to preserve their signal-to-noise ratio.[9] The down-state provided by K-complexes does this by reducing the strengths of synaptic connections that occur while an individual is awake.[1] Further, the recovery from the down-state they induce allows that "cortical firing 'reboots' in a systematic order" so that memory engrams encoded during neuronal firing can be "repeatedly practiced and thus consolidated".[1]

https://en.wikipedia.org/wiki/K-complex