Question: When was the sister of Theodora Porphyrogenita died who was reigned as Byzantine Empress alongside her sister?

Context paragraphs:
Theodora Porphyrogenita (11th century): Theodora Porphyrogenita (Greek: Θεοδώρα, "Theodōra" ; AD 980 – 31 August 1056) was a Byzantine Empress born into the Macedonian dynasty that had ruled the Byzantine Empire for almost two hundred years.  She was co-empress with her sister Zoë for two months in 1042 and sole empress regnant from 11 January 1055 to 31 August 1056.  She was the last of the Macedonian line, and upon her death the empire entered a period of decline that lasted until the ascension of Alexios I Komnenos in 1081.

Zoë Porphyrogenita: Zoë ( "life" ] ; 978 – June 1050) reigned as Byzantine Empress alongside her sister Theodora from April 19 to June 11, 1042.  She was also enthroned as the Empress Consort to a series of co-rulers beginning with Romanos III in 1028 until her death in 1050 while married to Constantine IX.

Bardas: Bardas (Greek: Βάρδας ; died 21 April 866) was a Byzantine noble and high-ranking minister.  As the brother of Empress Theodora, he rose to high office under Theophilos (r. 829–842).  Although sidelined after Theophilos's death by Theodora and Theoktistos, in 855 he engineered Theoktistos's murder and became the "de facto" regent for his nephew, Michael III (r. 842–867).  Rising to the rank of "Caesar", he was the effective ruler of the Byzantine Empire for ten years, a period which saw military success, renewed diplomatic and missionary activity, and an intellectual revival that heralded the Macedonian Renaissance.  He was assassinated in 866 at the instigation of Michael III's new favourite, Basil the Macedonian, who a year later would usurp the throne for himself and install his own dynasty on the Byzantine throne.

Theodora (wife of Romanos I): Theodora (Greek: Θεοδώρα , ] ; died 20 February 922) was a Byzantine Empress consort by marriage to Romanos I Lekapenos.

Rita of Armenia: Rita of Armenia (10/11 January 1278 – July 1333) was a Byzantine Empress consort.  She was a daughter of King Levon II of Armenia and Queen Keran.  She was the wife of Byzantine co-emperor Michael IX Palaiologos, making her a junior empress-consort of the Byzantine Empire.  In 1317, she became the only empress upon the death of the senior empress, Irene of Montferrat.  She was known as Maria in Constantinople.

Theodora (wife of Theophilos): Theodora (Greek: Θεοδώρα , ] c. 815 – after 867) was a Byzantine Empress as the spouse of the Byzantine emperor Theophilos, and regent of her son, Michael III, from Theophilos' death in 842 to 855.  For her restoration of the veneration of icons, which ended the Byzantine Iconoclasm, she is venerated as a saint in the Eastern Orthodox Church; her Feast Day is February 11.

Maria of Trebizond: Maria Megale Komnene (Greek: Μαρία Μεγάλη Κομνηνή ), known as Maria of Trebizond (Greek: Μαρία της Τραπεζούντας ), (died 17 December 1439) was a Byzantine Empress consort by marriage to the Byzantine emperor John VIII Palaiologos (r. 1425–1448).  She was the last empress consort of the Byzantine Empire.

Theodora (1921 film): Theodora (Italian: "Teodora" ) is a 1921 Italian silent film dramatization of the life of the Byzantine empress Theodora.

Theodora (given name): Theodora (Greek: Θεοδώρα , "Theodōra") is a feminine given name, the feminine version of Theodore, which derives from the Greek words "θεός ", "theos", "god" and "δῶρον ", "doron", "gift".  "Theodora" is first attested in Mycenaean Greek, written in the Linear B syllabic script, as 𐀳𐀃𐀈𐀨 , "te-o-do-ra".  The name Dorothy (Greek: Δωροθέα , "Dōrothea") contains the same word elements in reverse order.  It was the name of several saints and queens, including Theodora, a 6th-century Byzantine empress honored as a saint in the early Christian Church.  Teodora, a variant, is among the top 10 most popular names for girls born in Serbia between 2003-2005.

Anastasia the Patrician: Saint Anastasia the Patrician ("Anastasia Patricia"; fl.  567) was a Byzantine courtier and Saint.  She was the wife of a consul and a lady-in-waiting to the Byzantine empress Theodora.  Justinian I, Theodora's husband, pursued her, arousing Theodora's jealousy.  Anastasia tried to avoid any trouble and left for Egypt.  She arrived at a place called Pempton, near Alexandria, where she founded a monastery which would later be named after her.

Supporting paragraphs: Theodora Porphyrogenita (11th century) Zoë Porphyrogenita
Answer: June 1050