early 15c., "complex combination or intricate intermingling," from Latin complicationem (nominative complicatio), noun of action from past participle stem of complicare "to fold together, fold up, roll up," from com "with, together" (see com-) + plicare "to fold, weave" (from PIE root *plek- "to plait").
From 1690s as "an additional disorder which develops during the course of an existing one," hence, generally, "that which renders (an existing situation) complex, involved, or intricate."
Complication commonly implies entanglement resulting either in difficulty of comprehension or in embarrassment; complexity, the multiplicity and not easily recognized relation of parts; as business complications; the complexity of a machine; the complexity of a question of duty. [Century Dictionary]