Question: Who is the paternal grandmother of Zoë Porphyrogenita?

Kaoru Hatoyama
After the elections of 2009, she became more widely known as the grandmother of Prime Minister Yukio Hatoyama and his politician brother Kunio Hatoyama.
Mona Hopton Bell
Mona Hopton Bell( 1867- 1940) was a British artist, best known for her portraits of civic figures.
She was the grandmother of the painter Jean H. Bell.
Anne Denman
Anne Denman( 1587–1661) was born in Olde Hall, Retford, Nottinghamshire.
Through a fortunate second marriage with Thomas Aylesbury, she became the grandmother of Lady Anne Hyde, Duchess of York and great- grandmother of Queen Mary II and Queen Anne.
Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.
Tjuyu
Tjuyu( sometimes transliterated as Thuya or Thuyu) was an Egyptian noblewoman and the mother of queen Tiye, and the wife of Yuya.
She is the grandmother of Akhenaten, and great grandmother of Tutankhamun.
Hüma Hatun
Hüma Hatun (1410 ‒ September 1449) was the fourth wife of Ottoman Sultan Murad II and mother of Mehmed II and the grandmother of Bayezid II.
Zoë Porphyrogenita
Zoë Porphyrogenita ("life" ; 978 – 11 June 1050) reigned as Byzantine Empress from 11 November 1028 until her death in 1050.
She ruled alongside her three husbands, her adopted son Michael V, and her sister Theodora.
Zoë held actual power with Theodora for only two months between April and June 1042.
Zoë was born to Constantine VIII, who was nominal co-emperor to his brother Basil II.
Basil died when Zoë was 47, leaving the Byzantine throne entirely to her father.
As he had no sons, Constantine hoped to continue the dynasty by marrying off one of his daughters.
Zoë, aged 50, was married to Romanos Argyros.
Zoë and her husband took the throne three days later on her father's death.
The marriage was troubled and after five years Romanos III was found dead in his bath.
His death has been variously attributed to Zoë, her young lover Michael, or both.
They were married on the same day as the murder, and he was crowned emperor on the following day.
Seven years later, Zoë was persuaded to adopt her dying husband's nephew, also named Michael.
Once Michael V became emperor, he promptly exiled Zoë.
This action sparked a popular revolt which dethroned him and installed Zoë and Theodora as joint empresses.
After a two-month joint reign Zoë married a former lover who was installed as Constantine IX Monomachos, transferring power to him.
Eight years later, Zoë died aged 72.
Hubba bint Hulail
Hubba bint Hulail was the grandmother of Hashim ibn' Abd Manaf, thus the great- great- great- grandmother of the Islamic" Nabī"( Prophet) Muhammad ibn Abdullah.
Gülbahar Hatun (wife of Mehmed II)
Gülbahar Hatun( 1432 – 1492) was the consort of Sultan Mehmed II, and mother of Sultan Bayezid II of the Ottoman Empire and the grandmother of Selim I.
Constantine VIII
Constantine VIII ("Kōnstantinos VIII") (960 – 11 November 1028) was the Byzantine Emperor from 15 December 1025 until his death in 1028.
He was the younger son of Emperor Romanos II and Empress Theophano.
He was nominal co-emperor for 63 years from 962, successively with his father; stepfather, Nikephoros II; uncle (by marriage), John I; and brother, Basil II.
Basil II died childless in 1025 and thus left the rule of the Byzantine Empire in Constantine's hands.
Constantine had no interest in politics, statecraft or the military.
His brief reign is said to have been "an unmitigated disaster", sparking "a collapse of the military power of the Empire".
Constantine had no sons, so shortly before his death he married his daughter Zoë to his chosen successor Romanos Argyros.

Answer: Theophano