Final answer:
The two last Inca emperors were Wayna Qhapaq and his successor Atahualpa, the latter being the last ruling emperor at the time of the Spanish conquest. Túpac Amaru was a nominal leader installed by the Spaniards after the empire's fall and did not hold power in the same way.
Step-by-step explanation:
The Last Inca Emperors
The two last emperors of the Inca Empire were Atahualpa and his predecessor Wayna Qhapaq (also known as Huayna Capac). Atahualpa was the last ruling Inca emperor who was captured by the conquistador Francisco Pizarro in 1533 and executed a year later.
Although Túpac Amaru is often mentioned as the last Inca ruler, he was a puppet leader installed by the Spaniards and did not hold power like the emperors before him. The Inca Empire officially came to an end under Atahualpa's rule following a series of European conquests and internal strife that destabilized the empire.
Wayna Qhapaq led the empire through a period of expansion, but it was during Atahualpa's time that the Spanish began their conquest, leading to the eventual fall of the empire.
The empire had been significantly expanded earlier by Inca rulers such as Pachacuti and his son Tupac Inca Yupanqui, who are known for their military campaigns that extended the empire's reach. However, it's important to distinguish between these historical figures as founders and expanders of the empire and Atahualpa, who was an actual emperor at the time of the conquest.