AMC 12A 2025 (Problem 9)

Complex NumbersMedium

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?

\text{(A)}\;\frac{3}{4}

\text{(B)}\;1

\text{(C)}\;\frac{7}{5}

\text{(D)}\;\frac{3}{2}

\text{(E)}\;\frac{5}{3}