Final answer:
Francisco Pizarro defeated the Inca by killing a largely unarmed group and kidnapping and murdering their king, Atahualpa, despite taking a ransom. He used superior military tactics, deception, and the political instability of the Inca, augmented by alliances with indigenous tribes.
Step-by-step explanation:
Francisco Pizarro defeated the Inca primarily by killing a largely unarmed group and then kidnapping and murdering their king, Atahualpa. On November 16, 1532, Pizarro and his forces carried out a surprise attack against Atahualpa and his unarmed escort, slaughtering around 2,000 Inca on the spot. The Spaniards, displaying their military prowess and utilizing steel swords and horses, overwhelmed the Incas.
After accepting a large ransom of gold, Pizarro still executed Atahualpa, mirroring the approach of Cortés in Mexico. Pizarro's conquest included deceptive diplomacy and superior firepower, combined with the psychological impact of the horses and the timing of internal strife within the Inca Empire due to a civil war and the devastations of smallpox brought by Europeans.
After capturing the emperor, Pizarro went on to defeat the Inca capital, Cuzco, and founded the city of Lima. The collapse of the Inca leadership paved the way for Spanish control. Pizarro's victory was also aided by forming alliances with indigenous groups who were enemies of the Inca, leveraging their discontent to his advantage. Ultimately, this conquest led to Spain plundering the Inca wealth, the imposition of Catholicism, and the dominance of the Spanish language over indigenous languages.