*plek-

"associate in crime," 1580s, an unetymological extension of earlier complice "an associate or confederate" (early 15c.), from Old French complice "a confederate, partner" (not in a criminal sense), from Late Latin complicem (nominative complex) "partner, confederate," from Latin complicare "to involve," literally "fold together," from com "with, together" (see com-) + plicare "to fold, weave" (from PIE root *plek- "to plait"). Altered perhaps on model of accomplish, etc., or by assimilation of the indefinite article in a complice.

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").

The meaning "sincere hard effort" is from c. 1600. That of "a formal request to be hired for a job or paid position" is by 1851. The computer sense "program designed to carry out specific tasks or solve specific problems within a larger system" is a shortening of application program (1969).