Middle English, "associate, accomplice," borrowed from Anglo-French, borrowed from Late Latin complic-, complex "fellow-participant, partner, accomplice (in wrongdoing)," probably noun derivative of complicāre "to fold together, fold up, bundle, connect (to), cause to join" (going back to Latin, "to fold together"), after derivatives with the multiplicative suffixal element -plex, as in duplex "folded double, duplex entry 1" — more at complicate entry 2