What can you conclude from the fact that Constantine I moved the capital of the Roman Empire from Rome to Byzantium?

First of all. Constantine did not move the capital form Rome to Byzantium. Rome had already ceased to be the capital of the Roman Empire under his predecessor, Diocletian. Diocletian had created the tetrarchy (rule by four) with two senior emperors and two junrio ones. Each emperor had an imperial seat. The four capitals were Nicomedia (Izmit in north-western Turkey) Mediolanum (Milan, in northern Italy), Sirmium (Sremska Mitrovica in Serbia) and Augusta Trevorum (triers in south-western Germany). These cities were close to the frontiers of the empire, which had frequently come under attacks. Rome was side-lined because it was far from the frontiers.

The fact that Constantine chose Byzantium (which was only some 60 miles west of Nicomedia) as his capital show that it was still important to have a capital closer to the frontiers. The fact that Constantine wanted his own capital shows his determination to be recognised as the sole rue of the empire and his sue of Propaganda to bolster this. He brought the tetrarchy to an end by winning two civil wars and became the sole emperor. He dediced to bolster this by creating his own capital, which he named after himself (Byzantium was renamed Constantinople, which means city of Constantine). His new capital showed that he was in charge and was used as a symbol of the new dawn his rule would bring to the empire. The city was also given he honorary titles of 'the eastern Rome', 'the new Rome', 'alma Roma' and 'Roma Constantiniana)