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
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