In what year did the two branches of Christianity - Roman Catholic and Eastern Orthodox - formally split when the pope and patriarch excommunicated each other?

Answer 1

Roman Catholic AnswerThe estrangement and severance from the Holy See of what is now called the Eastern Orthodox Church was a gradual process extending over centuries. After a number of minor schisms, the first serious, thought short, break was that of Photius [857 A.D.]; from then on tension between East and West increased, and the schism of Cerularius occurred in 1054 A.D.. From then on the breach gradually widened and has been definitive since 1472. There was a formal union from the 2nd council of Lyons in 1274 until 1282 A.D., and a more promising one after the council of Florence from 1439 to 1472 A.D.. After the capture of Constantinople it was in the Turkish interest to reopen and widen the breach with the powerful Roman church; the patriarchates of Alexandria, Antioch, and Jerusalem were dragged into this policy, Russia and the Slav churches stood out the longest of any: none of these churches, except Constantinople itself in 1472 A.D., formally and definitely broke away from the unity of the Church. But in the course of centuries the schism has set and crystallized into a definite separation from the Holy See of many millions of people with a true priesthood and valid sacraments. The origins, causes and development of the schism are matters of much complication, still not fully unravelled.

from A Catholic Dictionary, Edited by Donald Attwater, Second Edition, revised.