Question

find all units of the ring of gaussian integers
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Answer 1

Answer:

hlo✔

Theorem

Let (Z[i],+,×) be the ring of Gaussian integers.

The set of units of (Z[i],+,×) is {1,i,−1,−i}.

Let a+bi be a unit of (Z[i],+,×).

Then a and b are not both 0 as then a+bi would be the zero of (Z[i],+,×).

Let α=a+bi be a unit of (Z[i],+,×).

Hence the set of units of (Z[i],+,×) is {±1,±i}.

be ☺

Answer 2

Answer:

set of units of (Z[i],+,×) is {±1,±i}.