The field is also a vector space over . Do not prove this fact. Prove that is isomorphic to the complex numbers as a real vector space.

So far, this is what I have. It's not much, but it's a start.

Let

I've been told that I'm to prove that this is one-to-one, onto, and linear.

That's about as much as I know. My brain's a little muddled at the moment due to a short bout of sickness, so I could use a hand.