Is the word completar the same in Brazilian and European Portuguese?

Yes

The word "completar" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The differences between the two dialects regarding this word are:

• Pronunciation: In Continental Portuguese, unstressed vowels are often reduced or even "swallowed" (e.g., the "e" in "completar" may be very closed or nearly silent), whereas Brazilian Portuguese tends to have more open and clearly articulated vowels.
• Syntax/Grammar: When expressing an ongoing action, Brazilians almost exclusively use the gerund (e.g., completando), while Portuguese people use the preposition "a" followed by the infinitive (e.g., a completar).
• Typical Usage: While "completar" is perfectly correct in both, a Portuguese person might more naturally use synonyms like "terminar" (to finish) or "preencher" (to fill out) depending on the context.

Brazilian Portuguese Examples

1. Estou completando o relatório agora. (I am completing the report now.)
2. Você precisa completar o seu cadastro. (You need to complete your registration.)
3. A água vai completar o nível do balde. (The water will complete the level of the bucket.)
4. Ele está completando a sua coleção de moedas. (He is completing his coin collection.)
5. Falta pouco para completar um mês de trabalho. (It is not long until one month of work is completed.)

Continental Portuguese Examples

1. Estou a terminar o relatório agora. (I am finishing the report now.)
2. Precisas de preencher o teu registo. (You need to fill out your registration.)
3. A água vai completar o nível do balde. (The water will complete the level of the bucket.)
4. Ele está a completar a sua coleção de moedas. (He is completing his coin collection.)
5. Falta pouco para completar um mês de trabalho. (It is not long until one month of work is completed.)