Final answer:
Ayatollah Khomeini demanded the return of the Shah for trial, a formal U.S. apology, and the return of funds for the hostages' release. The hostages were released following an agreement that involved unfreezing Iranian assets, coinciding with President Reagan's inauguration.
Step-by-step explanation:
Ayatollah Khomeini indicated he would release the American hostages under specific conditions. These included demanding the Shah be returned to Iran for trial and execution, a formal apology from the United States for its role in the 1953 coup that had placed the Shah in power, the return of millions of dollars believed the Shah had stolen from Iran, and the need for US-made spare parts and ammunition for Iran's military during the Iran-Iraq War. Negotiations for the release of hostages were tied to the Algiers Accords, which involved the unfreezing of Iranian assets and an embargo lift, among other agreements. The hostages were eventually released on January 20, 1981, immediately after Ronald Reagan was sworn in as president.