19. (Total: 12 points) Given that the complex number $z_1$ satisfies $(z_1 - 2)(1 + i) = 1 - i$ (where $i$ is the imaginary unit), and the imaginary part of complex number $z_2$ is 2, and $z_1 \cdot z_2$ is a real number, find $z_2$.
19. (Total: 12 points) Given that the complex number $z_1$ satisfies $(z_1 - 2)(1 + i) = 1 - i$ (where $i$ is the imaginary unit), and the imaginary part of complex number $z_2$ is 2, and $z_1 \cdot z_2$ is a real number, find $z_2$.