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, "a whole comprised of interconnected parts," from complex (adj.). Latin completus as a noun meant "a surrounding, embracing, connection, relation." Psychological sense of "connected group of repressed ideas" was established by C.G. Jung, 1907.
1550s, "net-like arrangement of threads, wires, etc., anything formed in the manner of or presenting the appearance of a net or netting," from net (n.) + work (n.). Extended sense of "any complex, interlocking system" is from 1839 (originally in reference to transport by rivers, canals, and railways). Meaning "broadcasting system of multiple transmitters" is from 1914; sense of "interconnected group of people" is by 1934 in psychology jargon.
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.