I have two sets of complex coordinates $(z1,z2)$ and $(y1,y2)$. I have the following relation between them 
$$
\frac{z1^* dz1+z2^* dz2}{1+\mid z1\mid^2+\mid z2\mid^2}=dy1+dy2
$$
Where, $*$ denotes complex conjugation and $\mid z\mid^2=z z^*$. I don't know the exact relation between $(z1,z2)$ and $(y1,y2)$. Is there a way to get the relation using the above condition?. I have no idea how to start. Please help!