The correct option is B) It began as a part of the Roman Empire.
The Byzantine Empire was also known as the Eastern Roman Empire that is why the correct option is that it began as a part of the Roman Empire. The name Byzantine came later from the capital city of the Empire which was Byzantium.
This empire lasted from 330 to 1453 C.E. Its territories expanded throughout the Balkans, Italy, Greece,Asia Minor ,and North Africa.
Although the Byzantine Empire received many aspects of the Greco-Roman culture,they managed to make a difference and not to be a copy of ancient Rome.