I am a bit confused by this question. The statement of the question tells me that $(x|Ty) = -(Tx|y)$ and that $B$ is an orthonormal basis. Also, that the field is $C$.
On my own, I have found that working with the given equality tells me that for $\alpha \in B$:
$\bar{a_i}$ $= -a_i$
(where $T\alpha$ $= \sum$$a_i\alpha_i$)
I also know that: $T\alpha_j$ $= \sum(T\alpha_j | \alpha_i) \alpha_i$
I am just not sure what this is telling me about the matrix $[T]_B$