Final answer:
The Macedonian king who conquered Greece was Philip II, who founded the League of Corinth and planned to attack the Persian Empire. His son, Alexander the Great, continued his legacy.
Step-by-step explanation:
The Macedonian king who conquered Greece was Philip II. After his victory at the Battle of Chaeronea in 338 BCE, he founded the League of Corinth, a federation of Greek city-states, establishing himself as the leader with the intent to launch a united Greek campaign against the Persian Empire. However, Philip II's assassination in 336 BCE prevented him from realizing his plan. His son, Alexander the Great, later adopted and accomplished this mission, leading to the spread of Greek culture across his vast empire.