I have two sets of complex coordinates $(z_1,z_2)$ and $(y_1,y_2)$. I have the following relation between them $$ \frac{\bar{z}_1 dz_1+\bar{z}_2 dz_2}{1+|z_1|^2+|z_2|^2}=dy_1+dy_2 $$ I don't know the exact relation between $(z_1,z_2)$ and $(y_1,y_2)$. Is there a way to get the relation using the above condition?