let $U_0=\{[z:w]:z\neq 0\}$ and $U_1=\{[z:w]:w\neq 0\}$, $(z,w)\in \mathbb{C}^2$,and $[z:w]=[\lambda z:\lambda w],\lambda\in\mathbb{C}^{*}$ is a point in $\mathbb{CP}^1$, the map is $\phi:U_0\rightarrow\mathbb{C}$ defined by $\phi([z:w])=w/z$
$\phi([z_1:w_1])=\phi([z_2:w_2])$ which implies $w_1/z_1=w_2/z_2$, but how can I conclude $w_1=w_2$ and $z_1=z_2$ to show $\phi$ injectuve?