So if and only if . Example 1 already matches the form, so you just look at it and say "yes". For example 2 you can do simple manipulation to get it into the form (3/2)+(8/2)*Sqrt(-5) which matches the form . Likewise for example 3. Example 4, let b = 0, which is acceptable. Example 5 is slightly trickier, just expand to get i*sqrt(-5) = i*i*sqrt(5) = -sqrt(5) which you should be able to see isnotin Q[sqrt(-5)].

Edit: Well I interchanged with without meaning to, but it should still be clear enough.