vervollständigen
to complete
To make something that is incomplete complete by adding the missing parts or information.
Bitte vervollständigen Sie das Formular mit Ihren persönlichen Daten.
Please complete the form with your personal details.

to complete
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to complete
To make something that is incomplete complete by adding the missing parts or information.
Bitte vervollständigen Sie das Formular mit Ihren persönlichen Daten.
Please complete the form with your personal details.

The word is easy to derive: the adjective 'vollständig' (complete) is turned into a verb with the prefix 'ver-'. So 'vervollständigen' (to complete) literally means to make something complete.
Ich muss meine Notizen für die Prüfung noch vervollständigen.
I still have to complete my notes for the exam.
'Vervollständigen' (to complete) begins with the prefix 'ver-' and is therefore an inseparable verb. The prefix is never separated from the rest of the verb in a sentence.
Er vervollständigte den Bericht mit den neuesten Zahlen.
He completed the report with the latest figures.
This verb is transitive and needs an accusative object. You ask: Whom or what are you completing? The answer is the thing being made complete.
Der Archäologe vervollständigte das zerbrochene Mosaik.
The archaeologist completed the broken mosaic.
'Vervollständigen' (to complete) is often used in formal or instructional contexts. Typical objects are: a sentence, a list, a collection, a form, or personal details.
Um die Anmeldung abzuschließen, müssen Sie Ihre Daten vervollständigen.
To finish the registration, you must complete your details.
to add / supplement
'ergänzen' and 'vervollständigen' are very close when something incomplete is made complete. 'ergänzen' emphasizes the individual addition: you add missing information or parts. 'vervollständigen' puts more emphasis on the result: afterward, something is complete. That is why you can often hear both words in similar situations. When the missing part is the focus, 'ergänzen' sounds more natural. When the finished whole is important, 'vervollständigen' is especially fitting.

Beim Termin vervollständigst du morgen die Unterlagen für den Antrag.
At the appointment tomorrow, you will complete the documents for the application.
Frau Schmidt ergänzt bei der Arbeit noch die Adresse des Kunden.
At work, Ms. Schmidt still adds the customer's address.