1610s, "to trick, deceive, cheat," from French intriguer (16c.), from Italian intrigare "to plot, meddle; perplex, puzzle," from Latin intricare "to entangle, perplex, embarrass" (see intricate).

Meaning "to plot or scheme" is recorded by 1714. That of "to excite curiosity" is from 1894 (OED calls this use "A modern gallicism"). It also could mean "carry on a clandestine or illicit sexual relationship" (1650s). The word appears earlier in English as entriken "entangle, ensnare; involve in perplexity, embarrass" (late 14c.), from Old French entrique or directly from the Latin verb. Related: Intrigued; intriguer; intriguing. Dutch intrigueren, German intriguiren are from French.

"like a maze, winding, intricate," 1570s, from maze (n.) + -y (2).

Japanese art of folding paper into intricate designs, 1956, from Japanese origami, from ori "fold" + kami "paper."

1620s, "to intertwine," from Latin complicatus "folded together; confused, intricate," past participle of complicare "to involve," literally "to fold together," from com "with, together" (see com-) + plicare "to fold, weave" (from PIE root *plek- "to plait"). Meaning "to make more complex or intricate" is recorded from 1832, from earlier sense "to combine in a complex way" (17c.). Related: Complicated; complicating.

1640s, figurative, "to guide, to lead, direct the course of, especially through an intricate or perilous passage;" 1690s in the literal sense "to conduct (a vessel) as a pilot," from pilot (n.) or from French piloter. Related: Piloted; piloting.

1640s, "composed of interconnected parts, not simple," past-participle adjective from complicate. Figurative meaning "not easy to solve, intricate, confused, difficult to explain or understand" is from 1650s. Related: Complicatedness.

1650s, "composed of interconnected parts, formed by a combination of simple things or elements," from French complexe "complicated, complex, intricate" (17c.), from Latin complexus "surrounding, encompassing," past participle of complecti "to encircle, embrace," in transferred use, "to hold fast, master, comprehend," from com "with, together" (see com-) + plectere "to weave, braid, twine, entwine," from PIE *plek-to-, suffixed form of root *plek- "to plait."

The meaning "involved, intricate, complicated, not easily analyzed" is first recorded 1715. Complex sentence, for one containing one or more subordinate clauses in addition to the principal clause, is attested from 1776.