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1985 AMC 12 Question 23

AMC12 · 1985 AMC 12

Question 23

If $$
\begin{aligned} x&=\frac{-1+i\sqrt3}{2},\\ y&=\frac{-1-i\sqrt3}{2}, \end{aligned}
$$ where $i^2=-1,$ then which of the following is not correct?
  1. $x^5+y^5=-1$
  2. $x^7+y^7=-1$
  3. $x^9+y^9=-1$
  4. $x^{11}+y^{11}=-1$
  5. $x^{13}+y^{13}=-1$