Sketch or graph the given region and its image for the following mapping:

1) |z| <= 1/2, | arg z | <= pi/8, w = z^2

2) |z| <= 1/2, Im z > 0, w = 1/z

3) 1/2 <= x <= 1, w = z^2

4) |z| < pi/4, 0 < y < 1, w =sin z

5) 0 <= x <= 2pi, 1 < y < 3, w = sin z

6) -1 <= x <= 2, |y| <= pi, w = e^z