word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
late 14c., "having no deficiency, wanting no part or element; perfect in kind or quality; finished, ended, concluded," from Old French complet "full," or directly from Latin completus, past participle of complere "to fill up, complete the number of (a legion, etc.)," transferred to "fulfill, finish (a task)," from com-, here probably as an intensive prefix (see com-), + plere "to fill" (from PIE root *pele- (1) "to fill").