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

Yes

The word "imaginar" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the pronunciation is typically more "syllable-timed," meaning the vowels are more open, clear, and elongated. In Continental Portuguese, the pronunciation is more "stress-timed," where unstressed vowels are often reduced, shortened, or almost swallowed, making the word sound more closed and clipped.

Brazilian Portuguese Examples

1. Não consigo imaginar minha vida sem café. (I can't imagine my life without coffee.)
2. Imagina se a gente ganhasse na loteria! (Imagine if we won the lottery!)
3. Você consegue imaginar o tamanho dessa bagunça? (Can you imagine the size of this mess?)
4. Eu não imaginava que você viria hoje. (I didn't imagine you would come today.)
5. É difícil imaginar como era a vida antigamente. (It's hard to imagine how life was in the past.)

Continental Portuguese Examples

1. Não consigo imaginar a minha vida sem café. (I can't imagine my life without coffee.)
2. Imagina se ganhássemos na lotaria! (Imagine if we won the lottery!)
3. Consegues imaginar o tamanho desta confusão? (Can you imagine the size of this mess?)
4. Não imaginava que viesses hoje. (I didn't imagine you would come today.)
5. Estou a imaginar o que poderá acontecer. (I am imagining what might happen.)