Which of the given sets are closed regions?
A. $(Re\ z)^2>1$
B. $0<\vert z - 2 \vert < 3$
C. $-1<\ Im\ z \le 1$
D. $\vert z \vert \ge 2$
E. $\vert z-1+i \vert \le 3$
F. $\vert Arg\ z \vert < \frac{\pi}{4}$