Iran has been a geographically distinct and culturally cohesive region throughout the study period. 1 CE At the beginning of the study period, this region, along with Iraq, was the heartland of the Parthian Empire. Since that time, Iran and Iranians have sometimes expanded outward to rule or settle in adjacent regions, and the names of its empires has changed with its ruling dynasties (Parthian, Sassanian, etc.), but the basic boundaries and ethnic identity of Iran has been stable. That's not to say there haven't been visitors.
7th century: The expansion of the Muslim Umma brought a new ruling class to the region - Arabs from the Arabian peninsula, who ruled the Ummayad and Abbasid Caliphates. If your family folklore indicates that you have Arabian blood, it is probably correct. These Arab empires stretched from Spain through Iran. If you had Arab-blooded ancestors in Iran in 1000, their ancestors could conceivably have been found anywhere in the lands ruled by the Umayyads and Abbasids in year CE 500.
11th Century: By this time, the Abbasid state was in decline, and many of its regions had gone independent. Shortly after AD 1000, the Seljuk Turks, a Central Asian nationality, migrated into Iran, the fertile crescent, and Anatolia, converted to Sunni Islam, and founded the Seljuk Empire, which replaced the Abbasid Caliphate. The Seljuks and their successors ruled Iran until the 13th century. if you had aristocratic Iranian ancestors in 1490 CE, their ancestors would probably have been living in both Iran, and Central Asia in CE 1000. Note that the Turks, themselves, originated in Mongolia a few centuries earlier, so your probable Turkish ancestors would have lived there, also, in CE 500.
13th Century: The Mongol expansion under Genghis Khan swamped Iran, which lived under Mongol rulers for over a century. Iran was a particular focus of interest for the Mongols because it enjoyed the highest standard of material culture in their empire. Thus traffic between Iran and the Mongol heartland was intense, and talented Iranians served in high posts throughout the empire. When the Mongol Empire disintegrated in the early 14th century, Iran's Mongol rulers assimilated with their former subjects. Thus, if you had ancestors in Iran in CE 1490, their ancestors could have lived anywhere in the Mongol Empire in CE 1000.)
During the late 14th century, a third Central Asian Turkish wave, the Timurids (after Timur - AKA Tamerlane), hit. Thus, if you had ancestors in Iran in 1490, there's a decent chance that you had them in Iran, Central Asia, and Mongolia in 1000.
16th Century: It happens again as the Central Asian Safavid Turks invade and take over. They are noteworthy for embracing Shiite Islam, the predominant religion of the Iranian people. They ruled until the 1740s. If your ancestors were aristocratic Iranians in 1800 CE, their ancestors probably lived both in Iran and Central Asia in 1490 CE.