A $n$ by $n$ hermitian matrix $A$ is such that
a) $A^{*}=A$ where $*$ represents complex conjugate transpose.
Now what does it mean for $B$ to be complex symmetric? Correct me if I am wrong on this but I think that
1) $B^{T}=B$ where $T$ represents transpose.
Both $A$ and $B$ are normal matrices so they both have an orthogonal set of eigenvectors that form a basis. Say for matrix $A$, these eigenvectors form a unitary matrix $U$ such that $UAU^{*}=D$ where $D$ is a diagonal matrix with eigenvalues along the diagonal.