Complex Geometry/Complex and holomorphic vector bundles

Exercises

 * 1) Let $$M := \mathbb C P^n$$ and define the tautological line bundle over $$\mathbb C P^n$$ to be the vector bundle $$\tau := \{([z], x) \in \mathbb C P^n \times \mathbb C| x \in [z]\}$$ with the projection $$\pi: ([z], x) \mapsto [z]$$. Find natural local trivialisations of $$\tau$$ that turn $$\tau$$ into a holomorphic line bundle.