The man Jesus died.. The Son of God was God and did not die. Jesus was man of very man and God of very God. We can not understand this in our human minds but the Son who is God in the Trinity did not die.
You are falling into the error of Nestorius, separating the man Jesus from the Divine Logos. The position you are espousing sets at naught the opening of John’s Gospel, as was recognized by the Fathers of the Third Ecumenical Council, who accepted St. Cyril of Alexandria’s critique of Nestorius, reasoned chiefly on the basis of the first chapter of John, in their anathema against Nestorius.