After he gained control of the roman empire, constantine moved the capital to
byzantium and renamed it constantinople.
rome and renamed it constantinople.
created a second capital in byzantium.
created a second capital in constantinople.

Correct

Additional details:

Constantine built his new capital city to resemble "Old Rome."  Constantine made his own capital city in monumental fashion, but wanted to give it also the prestige and aura of the Roman Empire. The building of Constantinople took several years, and Constantine modeled it after Rome, with government buildings designed in Roman style.

The existing city of Byzantium was the place Constantine built up and renamed after himself as Constantinople. (That's why the Eastern Roman Empire often is referred to as the Byzantine Empire.)

Today, Istanbul is the name of the city that was once Byzantium and then Constantinople.