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2025 AMC 12A Question 9

AMC12 · 2025 AMC 12A

Question 9

Let $w$ be the complex number $2 + i,$ where $i = \sqrt{-1}.$ What real number $r$ has the property that $r,$ $w,$ and $w^2$ are three collinear points in the complex plane?
  1. $\dfrac{3}{4}$
  2. $1$
  3. $\dfrac{7}{5}$
  4. $\dfrac{3}{2}$
  5. $\dfrac{5}{3}$