A question about convex domain in$\mathbb{C}^n$

Question

I'm reading Grauert's book：From Holomorphic Functions to Complex Manifolds. The fourth problem in the exercise on page 8,it needs us to prove that a domain $G$ is convex if and only if for every $z\in\partial G$ there is an affine linear function $\lambda:\mathbb{C}^n\rightarrow\mathbb{R}$ with $\lambda(z)=0$ and $\lambda|_{G}<0$.I don't know how to prove this characterization of convexity of domain,I think it is easy but I need some hint.