Question 22What is the greatest possible area of the triangle in the complex plane with vertices $2z,$ $(1+i)z,$ and $(1-i)z,$ where $z$ is a complex number satisfying $|4z - 2| = 1?$$\dfrac{1}{4}$$\dfrac{1}{2}$$\dfrac{9}{16}$$\dfrac{3}{4}$$1$