1972 AHSME Problems/Problem 3

Revision as of 01:53, 7 November 2020 by Lopkiloinm (talk | contribs) (Solution)

Problem 3

If $x=\dfrac{1-i\sqrt{3}}{2}$ where $i=\sqrt{-1}$, then $\dfrac{1}{x^2-x}$ is equal to

$\textbf{(A) }-2\qquad \textbf{(B) }-1\qquad \textbf{(C) }1+i\sqrt{3}\qquad \textbf{(D) }1\qquad  \textbf{(E) }2$

Solution

Using DeMoivre's theorem, we can calculate $x^2=\frac{1+i\sqrt{3}}{2}$ The denominator is therefore $-1$ which makes the answer $\boxed{\textbf{(C) }-1$ (Error compiling LaTeX. Unknown error_msg). ~lopkiloinm