Meaning "feat, achievement" is c. 1400. Sense evolution is from "unfolding" to "bringing out" to "having advantage" to "achievement." Related: Exploits.
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.
Meaning "to involve something unstated as a logical consequence" first recorded c. 1400; that of "to hint at" is from 1580s. Related: Implied; implying. The distinction between imply and infer is in "What do you imply by that remark?" but, "What am I to infer from that remark?" Or, as Century Dictionary puts it, "An action implies ability or preparation, but involves consequences."
Imply, which is the same word, retains more of the original sense. Sense of "hire, engage" first recorded in English 1580s, from meaning "involve in a particular purpose," which arose in Late Latin. Related: Employed; employing; employable.
late 14c., replicacioun, "an answer, a verbal response;" also, specifically in law, "a rejoinder, legal reply" (third step in the pleadings in a common-law action), from Anglo-French replicacioun, Old French replicacion "reply, answer," from Latin replicationem (nominative replicatio) "a reply, repetition, a folding back," noun of action from past-participle stem of replicare "to repeat, reply.
This is etymologically "to fold back," from re- "back, again" (see re-) + plicare "to fold" (from PIE root *plek- "to plait"). The meaning "a copy, reproduction" is recorded by 1690s. The sense of "process by which genetic material copies itself" is from 1948.
mid-12c., multeplien, "to cause to become many, cause to increase in number or quantity," from Old French multiplier, mouteplier (12c.) "increase, get bigger; flourish; breed; extend, enrich," from Latin multiplicare "to increase," from multiplex (genitive multiplicis) "having many folds, many times as great in number," from combining form of multus"much, many" (see multi-) + -plex "-fold," from PIE root *plek- "to plait."
Intransitive sense of "grow or increase in number or extent" (especially "to have children, produce offspring") is from mid-14c. Mathematical sense "perform the process of multiplication" is attested from late 14c. Related: Multiplied; multiplying.
early 15c., "the bringing of something to bear on something else," from Old French aplicacion (14c.), from Latin applicationem (nominative applicatio) "a joining to, an attaching oneself to; relation of a client to a patron," noun of action from past-participle stem of applicare "attach to, join, connect," from ad "to" (see ad-) + plicare "to fold" (from PIE root *plek- "to plait").
Meaning "sincere hard effort" is from c. 1600. Meaning "a formal request to be hired for a job or paid position" is by 1851. Computer sense "program designed to carry out specific tasks or solve specific problems within a larger system" is a shortening of application program (1969).
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]
1590s, "embarrass, puzzle, bewilder, fill (someone) with uncertainty," evidently a back-formation from perplexed, a variant of the adjective perplex (late 14c.), "perplexed, puzzled, bewildered," from Latin perplexus "involved, confused, intricate;" but Latin had no corresponding verb *perplectere. The Latin compound would be per "through" (from PIE root *per- (1) "forward," hence "through") + plexus "entangled," past participle of plectere "to twine, braid, fold" (from suffixed form of PIE root *plek- "to plait").
The form of the English adjective began to shift to perplexed by late 15c., probably to conform to other past-participle adjectives, and the adjective perplex became obsolete from 17c. The verb is the latest attested of the group. The sense of "make intricate, involve, entangle, make difficult to be understood" is from 1610s. Related: Perplexing, which well describes the history of the word; perplexingly.