1940, in reference to U.S. cartoonist Reuben Lucius Goldberg (1883-1970) who devised fantastically complex gadgetry to accomplish simple tasks. His British counterpart was Heath Robinson (1872-1944).
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]
"act of castrating," early 15c., castracioun, from Latin castrationem (nominative castratio), noun of action from past-participle stem of castrare "to castrate, emasculate," supposedly from a noun *castrum "knife, instrument that cuts," from PIE root *kes- "to cut." Freud's castration complex is attested from 1914 in English (translating German Kastrationsangst).
late 14c., "mathematician, one who calculates," from Latin calculator, from calculatus, past participle of calculare "to reckon, compute," from calculus "reckoning, account" (see calculus). Of mechanical adding machine contraptions, from 1784. Of electronic ones, from 1946.
Electronic calculator uses 18,000 tubes to solve complex problems [Scientific American headline, June 1946]