Degree of a curve in terms of positive line bundle

Question

Let $C$ be a smooth complex algebraic curve and $S$ a smooth complex algebraic surface. Let also $$ f: C \longrightarrow S $$

be an holomorphic map. I'm trying to prove that $$ \deg f(C) = \deg f^* \mathcal{L}$$ for $\mathcal{L}$ a big line bundle.