Let $d \in Z$ be an integer with $\sqrt{d} \notin Q$ (e.g. d = -3, -2, -1, 2, 3, 5).
We consider the set: $Q(\sqrt{d})={(a+b\sqrt{d} \in C | a,b \in Q)}$

a) Show that:
The connections of $(C,+,•)$ are inherited by $Q(\sqrt{d})$, i.e. the restrictions of the connections + and • on $Q(\sqrt{d})$x$Q(\sqrt{d})$ are internal connections in $Q(\sqrt{d})$.

b) Show that:$(Q(\sqrt{d}),+,•)$ is a field.