Final answer:
The Swahili coast of East Africa and the ports on the western coast of India, specifically in the Sultanate of Gujarat, are two regions of the Indian Ocean where merchants continued to flourish even after Europeans arrived.
Step-by-step explanation:
Two regions of the Indian Ocean where merchants continued to flourish even after Europeans arrived are the Swahili coast of East Africa and the ports on the western coast of India, such as those in the Sultanate of Gujarat.
The Swahili city-states along the East African coast were important hubs in the trade between East and West, connecting Africa to South and East Asia.
These city-states participated in oceanic trade with the Arabian Peninsula, India, and places farther east. Similarly, the ports on the western coast of India, especially in Gujarat, continued to thrive in the Indian Ocean trade network, attracting both European explorers and Indian dynasties.