Final answer:
Francisco Pizarro conquered Peru in 1532, exploiting a civil war and the impact of smallpox on the native population. He captured and executed Atahualpa, the Inca emperor, and founded Lima in 1535. Pizarro's control ended with his assassination in 1541.
Step-by-step explanation:
Francisco Pizarro, a Spanish conquistador, using trickery and deceit, conquered the Incas of Peru in 1532. Pizarro, who had been drawn by the rumors of immense wealth in the region and had even been named the governor of Peru in 1529, reached Peru with a small army and took advantage of the internal strife within the Inca Empire. Pizarro captured and eventually executed the Inca emperor, Atahualpa, despite Atahualpa's offer to fill a room with gold and two with silver in exchange for his freedom. Pizarro proceeded to establish control over the Inca capital, Cuzco, and in 1535, he founded the city of Lima, consolidating Spanish power in the region.