bethrathgeb6542 bethrathgeb6542
  • 25-05-2023
  • Mathematics
contestada

(a) Show that in C, Q(i) = {a+bi: a, b e Q} and Q(√5) = {a+b√√5: a, b € Q}. (b) Show that Q(i) and Q(√5) are isomorphic as vector spaces over Q, but not isomorphic as fields. (Hint: For the second part, suppose there is a field isomorphism y: Q(i) -Q(√5) and consider (1).)

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