Final answer:
Portugal wanted to trade in the Indian Ocean network primarily to tap into the lucrative spice trade, weaken the Muslim world, and strengthen the Christian world. Their desire for wealth and religious motives were driving forces behind their exploration and trade endeavors.
Step-by-step explanation:
The Portuguese wanted to trade in the Indian Ocean network primarily because of their desire to tap into the lucrative spice trade. The spice trade, which included items such as cloves, pepper, and ginger, originated in Asia and made its way through India before reaching European markets. By establishing trade routes in the Indian Ocean, Portugal aimed to enrich their own nation, weaken the Muslim world, and strengthen the Christian world.
The promise of great wealth and the desire for religious completion were driving forces behind Portugal's exploration and trade endeavors. The possibility of gaining riches from the spice trade and diverting it from overland routes to a European sea trade were major incentives for the Portuguese to explore the coast of Africa in search of a route to India.
In addition, the Portuguese attempted to increase their revenues by demanding that ships trading in the Indian Ocean carry a document known as a cartaz, bearing the Christian cross. Ships without the cartaz had their cargoes seized and were sunk. This further enabled Portugal to dominate Indian Ocean trade and benefit from increased commerce for its merchants in the ports it controlled.
Overall, Portugal's desire for wealth, religious motives, and aspirations of dominating the spice trade were key factors that drove their interest in establishing trade in the Indian Ocean network.