Origins
The verb 'complicate' is one of the 'plicāre' family members that entered English through the front door of learned Latin borrowing rather than through the servants' entrance of Old French phonological erosion. While 'apply,' 'comply,' 'imply,' and 'reply' all had their '-plicāre' roots ground down to '-ply' during centuries of French spoken transmission, 'complicate' was borrowed directly from the Latin past participle 'complicātus' in the early seventeenth century, preserving the full '-plicate' form.
Latin 'complicāre' combined 'com-' (together) with 'plicāre' (to fold), producing the literal meaning 'to fold together.' In classical Latin, the word described the physical act of interweaving, entangling, or combining multiple things into a single mass. Pliny used it for the coiling of serpents; legal writers used it for the intertwining of legal claims and obligations.
The extension from physical entanglement to conceptual difficulty is natural and was already underway in Latin. When multiple strands are folded together, the result is hard to untangle — a complicated thing is, etymologically, a thing whose elements have been so thoroughly folded into each other that separating them is difficult. This metaphor of difficulty as entanglement persists in English: we speak of 'tangled' situations, 'knotty' problems, and 'unraveling' mysteries.
Proto-Indo-European Roots
The relationship between 'complicate' and 'complex' is particularly instructive. 'Complex' comes from Latin 'complexus' (encompassed, embraced), past participle of 'complecti' (to encircle, embrace), from 'com-' (together) + 'plectere' (to weave, braid). Both 'plicāre' (to fold) and 'plectere' (to weave) descend from PIE *pleḱ- (to plait), so 'complicate' and 'complex' are etymological cousins — both describe things woven or folded together — but they arrived in English by different Latin paths.
The word 'accomplice' reveals another branch of this entangled family. An accomplice was originally a 'complice' (from Old French 'complice,' from Latin 'complicem,' accusative of 'complex' — here used as a noun meaning 'a person folded together with another'). English added the 'a-' prefix by analogy with 'accompany' and other words, creating 'accomplice' — literally, someone who is folded together with you, i.e., entangled in the same enterprise. The criminal connotation was not original; in medieval French, a 'complice' could be any partner or associate.
In modern medical usage, 'complications' — unforeseen problems arising during treatment — preserves the original sense of unwanted entanglement. A medical complication is an additional condition that folds itself into the existing situation, making the whole picture harder to address. The word's journey from Roman descriptions of physical folding to modern clinical vocabulary spans two millennia but maintains a consistent core metaphor.