Multiplying by purely complex exponential is basically a phase shift. If you shift original image, the amplitude of its frequency components remains the same, the only thing that changes is the phase of those components.
Shifting is done by moving the origin point of the image. If $f(x,y)$ is your original image, then $f(x+x_0,y+y_0)$ is your spatially shifted image where point of image originally located at $(0,0)$ is now located at $(x_0,y_0)$.