Bilinear form can be written as sum of hermitian and symmetric C bilinear form

Question

Suppose $g : E \times E \rightarrow \mathbb{C}$ is $\mathbb{R} $ bilinear.Show that there exists a hermitian form $h$ on $E$ and a symmetric $\mathbb{C}$-bilinear form $\psi$ on $E$ such that $2ig= h+ \psi$.

Can I consider $h =i(g(x,y)-g(y,x))$ and $\psi = i(g(x,y)+g(y,x))$ ?? Natural guess is this but I am not able to conclude anything. Thanks in advance