Ah! Thank you so much! Here's the answer for anyone who comes looking:Good, except for one little point:
[imath](a + bi)^2 = a^2 + 2abi + i^2b^2 = a^2 + 2abi - b^2[/imath]
What I'd do from here is solve [imath]2ab = 14[/imath] for b in terms of a and plug that into the [imath]a^2 - b^2 = 48[/imath] equation to get a.
-Dan