'Complicate' is Latin for 'folded together' — from 'plicare' (to fold). A tangle of layered folds.
To make something more difficult or confusing by introducing additional elements; to entangle or interweave.
From Latin 'complicātus,' past participle of 'complicāre' (to fold together, to entwine, to entangle), composed of 'com-' (together, with) + 'plicāre' (to fold). The PIE root is *plek- (to plait, to pleat, to fold), one of the richest roots for physical and conceptual entanglement in Indo-European. It yields Greek 'plekein' (to plait, to braid), Latin 'plectere' (to braid, to weave), Lithuanian 'pinti' (to braid), and Old Norse 'fletta' (to braid). The visual metaphor of 'complicāre' is precise: threads
An 'accomplice' is literally someone 'folded together with' you in a crime — from Latin 'complicāre.' The word was originally 'complice' (from Old French), meaning a partner or associate; the 'a-' prefix was added in English by false analogy with words like 'accompany.' A complicated plan and an accomplice are both