Suppose $\phi:\mathbb{C}^2\longrightarrow\mathbb{C}^2$ be an entire map (i.e, the components of $\phi$ are entire in each variable separately) with $\phi_1$,$\phi_2$ as its components satisfying $$|\phi(z,w)|^2 - |(z,w)|^2\leq \operatorname{Im}(\phi_1\overline{\phi_2})-\operatorname{Im}(z\overline{w})$$ Then what would be the formula of $\phi$? Or how does $\phi$ look like?
thanks in advance, I need a hint at least.