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

Yes

The spelling, meaning, and grammatical function of "imediatamente" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated, making the syllables distinct. In Continental Portuguese, there is a significant phenomenon of vowel reduction or elision, where unstressed vowels (especially the "e" at the end) are much more "closed" or almost silent, making the word sound more "clipped."

Brazilian Portuguese Examples

1. Eu preciso que você faça isso imediatamente. (I need you to do this immediately.)
2. O médico chegou imediatamente após o chamado. (The doctor arrived immediately after the call.)
3. Por favor, saia da sala imediatamente. (Please, leave the room immediately.)
4. Precisamos resolver esse problema imediatamente. (We need to resolve this problem immediately.)
5. Ela respondeu à minha mensagem imediatamente. (She replied to my message immediately.)

Continental Portuguese Examples

Note: While "imediatamente" is used in Portugal, a Portuguese person would often naturally use alternatives like "já," "logo," or "sem demora" in casual or even standard speech to express the same idea.

1. Eu preciso que faças isso já. (I need you to do this right now.)
2. O médico chegou num instante. (The doctor arrived in an instant.)
3. Por favor, sai da sala logo. (Please, leave the room right away.)
4. Temos de resolver isto sem demora. (We have to resolve this without delay.)
5. Responde-me imediatamente. (Reply to me immediately.)