Final answer:
The United States gained complete control of the Mississippi River and New Orleans in 1803 through the Louisiana Purchase, which was vital for trade and expansion. Hence, the correct answer is option (a).
Step-by-step explanation:
The United States gained complete control of the Mississippi River and New Orleans in 1803. This acquisition happened through the Louisiana Purchase, engineered by President Thomas Jefferson. New Orleans, which had been under French and Spanish control at various times, was crucial for its strategic location and was essential for the exports of cotton and other goods from the American South. With the Louisiana Purchase, not only did the United States acquire New Orleans, but it also doubled in size, vastly expanding its territory into what was then the western frontier.
During the Civil War, Union forces captured New Orleans in 1862, and by 1863 they had firm control over much of the Mississippi River. However, the essential control over the river and New Orleans was obtained in 1803 with the Louisiana Purchase, which allowed for American expansion and secured the crucial trade route.