Final answer:
The correct answer is a. The capture of Mesopotamia in 1534 gave the Ottoman Empire access to the Persian Gulf, an important maritime gateway for trade and strategic military movements during that period.
Step-by-step explanation:
The capture of Mesopotamia was a strategic conquest for the Ottoman Empire, providing them with access to vital trade routes and territorial expansion. Mesopotamia is defined by its two great rivers, the Tigris and Euphrates, which flow into the Persian Gulf. During the peak of the Ottoman Empire under Sultan Suleiman I, the Ottomans expanded their territory into various regions including Egypt and North Africa. With Mesopotamia under Ottoman control, they gained direct access to the Persian Gulf, a crucial maritime gateway for oceangoing vessels and, historically, a region of strategic economic importance that connected with the trade routes to the Indian Ocean. The Persian Gulf remains one of the world's most important choke points to this day, providing the only sea passage from the Gulf to the open ocean.
By controlling Mesopotamia and thus having access to the Persian Gulf, the Ottomans were better positioned to affect sea trade and exert their power over the Indian Ocean as they contended with other powers, such as the Portuguese.