Gaussian Integers with Norm 1 are Units
s23 math 302 quiz 09 problem 02
We give two different proofs that a Gaussian integer with norm 1 is a unit. The first proof utilizes the rectangular definition of the norm, i.e., N(a+bi) = a² + b². The second (and more elegant) proof utilizes the conjugate definition of the norm, i.e., N(z) = zz̅.
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