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Abstract Algebra Help

Question 1(a) Show that the ring Q[i], where Q is the field of rational numbers, and i2 = -1, is a (commutative)field. (Hint: give brief reasons for things like associativity, distributivity, inverses.)(b) Is the cardinality, |Q[i]|, of this field countable? (Hint: if so, this is equivalent to establishing abijection between Q[i] and a known countable set such as Z or Q.)(c) Is the cardinality of C, the complex numbers, countable? (Yes or no)(d) Explain why the fields Q[i] and C…
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