AMC 12 2025 Part B Problem 22

What is the greatest possible area of the triangle in the complex plane with vertices 2z, (1+i)z, and (1-i)z, where z satisfies |4z-2|=1?

Answer Choices:

A. \dfrac{1}{4}

B. \dfrac{1}{2}

C. \dfrac{9}{16}

D. \dfrac{3}{4}

E. 1