Solution
= Solution
Under the given <rotation>, $\bar z=\bar\alpha\bar w$ and $z\bar z=|\alpha|^2w\bar w=w\bar w$. Collecting terms gives
$$
a w\bar w+b\bar\alpha\bar w+\bar b\alpha w+c=0.
$$
Since $\overline{b\bar\alpha}=\bar b\alpha$, the transformed coefficients are
$$
\boxed{A=a,\qquad B=b\bar\alpha,\qquad C=c}.
$$