Thread: Q [sq rt 3 +i] is a unit

Problem: Every nonzero element of Q [sq rt 3 + i] is a unit. Prove answer?

Originally Posted by chadlyter

Problem: Every nonzero element of Q [sq rt 3 + i] is a unit. Prove answer?

Since
sqrt(3)+i
Is algebraic over Q.
Because it is a zero of,
x^4 - 2x^2-8

It means that,
Q[sqrt(3)+i]
Simple field extension over Q.

Thus, it is a field and hence, all non-zero elements are units.

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