"His work is complete now."
Translation:Son travail est complet maintenant.
"compléter" means to finish as in "j'ai compléter mes devoirs" means "I have finished my homework." It has nothing to do with giving complements or complementing. The only time it has the meaning of complementing is when it is used reflexively as in "Le vin et le fromage se complètent parfaitement."
Sorry, but that is no right: we never say "j'ai complété mes devoirs" to mean that we have finished our homework.
"I complemented the file with a copy of my passport" = "j'ai complété le dossier avec une copie de mon passeport".
"Tomorrow I will add a photo and the file will be completed" = "demain j'ajouterai une photo et le dossier sera complet" (not complété).
Actually, it is used that way. Here's an example from Word Reference.com.
compléter vtr (parachever) complete, conclude vtr finish off vtr phrasal sep La police s'active pour compléter son enquête. The police are hurrying to complete their investigation.
Notice that "finish off" is one of the meanings.
Note, though, that your exemple is not "complete":
"the police s'active pour compléter son enquête par l'audition d'autres témoins"
It means that they are adding elements to their investigation, not that the investigation will then be finished.
verb: compléter (= to add elements)
noun: un complément (= adjunct)
adjective: complet, complète, complets, complètes = complete, full, comprehensive, total, absolute.
adverb: complètement = completely, totally, fully...