$12 \cdot 10$ If $x=\frac{1-i \sqrt{3}}{2}$ where $i=\sqrt{-1}$, then $\frac{1}{x^{2}-x}$ equals
(A) -2 .
(B) -1 .
(C) $1+i \sqrt{3}$.
(D) 1 .
(E) 2 .
(23rd American High School Mathematics Examination, 1972)
[Solution] From $x^{2}-x$
$$
\begin{array}{l}
=\frac{1}{4}(1-i \sqrt{3})^{2}-\frac{1}{2}(1-i \sqrt{3}) \\
=\frac{1}{4}(-2-2 i \sqrt{3})-\frac{1}{2}(1-i \sqrt{3}) \\
=-1,
\end{array}
$$

Therefore, the reciprocal of $x^{2}-x$ is still -1. Hence, the correct choice is $(B)$.