complete / completely
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completely
Completely, entirely, without anything left over. The word is used both for material things and for abstract matters such as feelings or doubts.
Nach der langen Wanderung waren wir restlos erschöpft.
After the long hike, we were completely exhausted.
The word is made up of 'Rest' (remainder) and the ending '-los' (-less). The ending '-los' means 'without', so 'restlos' literally means 'without a remainder'.
Bitte esst den Kuchen restlos auf, damit wir nichts wegwerfen müssen.
Please eat up the cake completely so we don't have to throw anything away.
'Restlos' is often used like an adverb to intensify another word. It then means 'völlig' (totally) or 'komplett' (completely) and makes the statement stronger.
Das Konzert war schon nach wenigen Stunden restlos ausverkauft.
The concert was completely sold out after just a few hours.
Common combinations are 'restlos begeistert sein' (to be completely thrilled), 'restlos überzeugt sein' (to be completely convinced), 'etwas restlos aufklären' (to fully solve/clarify something), or 'etwas restlos aufessen' (to eat something up completely).
Die Polizei konnte den Fall restlos aufklären.
The police were able to fully solve the case.
completely
Völlig and restlos can both intensify complete conviction or agreement. Völlig mainly emphasizes the high degree, while restlos highlights that no doubt or reservation remains. Use völlig for the strength of a reaction and restlos when complete inner agreement without any qualification is meant.
Nach dem Gespräch war ich restlos überzeugt von dem Plan.
After the conversation, I was completely convinced by the plan.
Nach dem Gespräch war ich völlig überzeugt von dem Plan.
After the conversation, I was completely convinced by the plan.
