[QUOTE=beta12;24319]1) Which of the following are quadratic integers in Q[sqrt(-5)]?

a) 3/5

b) (3+8sqrt(-5))/5

c) i*sqrt(-5)

Again, use what I said before, namely that,

forms a basis for the field viewed as a vector space over .

We note that,

Meaning, that the rationals are contained in this simple extension.

a)Yes, as just explained all rationals are contained thin this field.

b)Yes, it is so if you select as a linear combination for then it works!

c)No, unless you are asking for .