Question: What year did the Ottomans complete their conquest of the Byzantine Empire?
About the article "Turkey", section "The Seljuks and the Ottoman Empire".

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The Fall of Constantinople (, '; Conquest of Istanbul) was the capture of Constantinople, the capital of the Eastern Roman (Byzantine) Empire, which occurred after a siege by the invading Ottoman Empire, under the command of 21-year-old Ottoman Sultan Mehmed II, against the defending army commanded by Byzantine Emperor Constantine XI Palaiologos.
The siege lasted from Friday, 6 April 1453 until Tuesday, 29 May 1453 (according to the Julian calendar), when the city fell and was finally conquered by the Ottomans.
The capture of Constantinople (and two other Byzantine splinter territories soon thereafter) marked the end of the Roman Empire, an imperial state which had lasted for nearly 1,500 years.
The Ottoman conquest of Constantinople also dealt a massive blow to Christendom, as the Ottoman armies thereafter were free to advance into Europe without an adversary to their rear.
After the conquest, Sultan Mehmed transferred the capital of the Ottoman Empire from Adrianople to Constantinople.
Several Greek and non-Greek intellectuals fled the city before and after the siege, with the majority of them migrating particularly to Italy, which helped fuel the Renaissance.
The conquest of the city of Constantinople and the end of the Byzantine Empire marks, for some historians, the end of the Middle Ages. 
The Fall of Gallipoli was the siege and capture of the Gallipoli peninsula, formerly under Byzantine occupation, by the Ottoman Turks in March 1354.
After suffering a half-century of a string of defeats at the hands of the Ottomans, the Byzantine Empire had lost nearly all of their possessions in Anatolia.
Access to the Aegean and Marmara meant that the Ottomans could now implement the conquest of the Peloponnese and Greece, and could advance further north into Serbia and Hungary. 
Turkish architecture is the architecture of the Ottoman Empire which emerged in Bursa and Edirne in 14th and 15th centuries.
The architecture of the empire developed from the earlier Seljuk architecture and was influenced by the Byzantine architecture, Iranian as well as Islamic Mamluk traditions after the conquest of Constantinople by the Ottomans.
For almost 400 years Byzantine architectural artifacts such as the church of Hagia Sophia served as models for most of the Ottoman mosques. 
Things went worse for Byzantium during the civil wars that followed after Andronikos III died.
A six-year long civil war devastated the empire, allowing the Serbian ruler Stefan IV Dushan (r. 1331–1346) to overrun most of the Empire's remaining territory and establish a short-lived "Serbian Empire".
In 1354, an earthquake at Gallipoli devastated the fort, allowing the Ottomans (who were hired as mercenaries during the civil war by John VI Kantakouzenos) to establish themselves in Europe.
By the time the Byzantine civil wars had ended, the Ottomans had defeated the Serbians and subjugated them as vassals.
Following the Battle of Kosovo, much of the Balkans became dominated by the Ottomans.
The Byzantine emperors appealed to the West for help, but the Pope would only consider sending aid in return for a reunion of the Eastern Orthodox Church with the See of Rome.
Church unity was considered, and occasionally accomplished by imperial decree, but the Orthodox citizenry and clergy intensely resented the authority of Rome and the Latin Rite.
Some Western troops arrived to bolster the Christian defence of Constantinople, but most Western rulers, distracted by their own affairs, did nothing as the Ottomans picked apart the remaining Byzantine territories.
Constantinople by this stage was underpopulated and dilapidated.
The population of the city had collapsed so severely that it was now little more than a cluster of villages separated by fields.
On 2 April 1453, Sultan Mehmed's army of some 80,000 men and large numbers of irregulars laid siege to the city.
Despite a desperate last-ditch defence of the city by the massively outnumbered Christian forces (c. 7,000 men, 2,000 of whom were foreign), Constantinople finally fell to the Ottomans after a two-month siege on 29 May 1453.
The last Byzantine Emperor, Constantine XI Palaiologos, was last seen casting off his imperial regalia and throwing himself into hand-to-hand combat after the walls of the city were taken. 
The Battle of Pelekanon was the first engagement in which a Byzantine Emperor encountered an Ottoman Bey.
The battle's moral effect was more important than the battle itself; the heavy-armed and disciplined Greeks had fled before the light-armed and irregular Turks; the spirit of the Greek Emperor and of the Greek nation was broken.
A campaign of restoration was aborted.
Never again did a Byzantine army attempt to regain territory in Asia.
The former imperial capitals of Nicomedia and Nicaea were not relieved and the maintenance of Imperial control across the Bosphorus was no longer tenable.
The Ottomans conquered Nicaea in 1331 and Nicomedia in 1337, thus building up a strong base from which they eventually swept away the Byzantine Empire as a whole.
The inhabitants of Nicaea and Nicomedia were quickly and willingly incorporated into the growing Ottoman nation, and many of them had already embraced Islam in 1340.
With the capture of these cities and the annexation of the Beylik of Karasi in 1336, the Ottomans had completed their conquest of Bythinia and the north-western corner of Anatolia.