No, this is not correct. WLOG means: I assume one of the possible cases, but the proof works the same way for other cases. But that's not true here. The proof, as shown, only works for a>b>0, it does not work (without extra work or explanation) for a<b. The proof for a<b is similar, but not the same.
[And it certainly does not show it for a,b element of C]
WLOG just means the other cases follow from the one case. There is no implication about how hard it is to get to the other cases, although generally it is easy and you don't bother spelling it out exactly.
