You proved that 2 is irreducible. You can show that the other two are irreducible by a similar argument. If

for non-units, then by taking norms

. Notice that

. Let

then

. For this to be less than

it is necessary for

. Therefore,

must be a real number. By a similar argument

must be a real number. However, it is impossible to have

to be an imaginary number. Thus, it is not possible to write

for non-units.

Say that

for non-units. By taking norms,

. Thus, we require that

. If

then

. We cannot have

so

. Likewise for

. If

then

which is a contradiction. Therefore,

, and now repeat the same argument as above.