Final answer:
Yes, the image of a distant quasar can be split into several images by the gravitational field of a foreground cluster, in a process known as gravitational lensing.
Step-by-step explanation:
The statement that the image of a distant quasar can be split into several images by the gravitational field of a foreground cluster is true. This phenomenon is known as gravitational lensing, and it occurs when the massive foreground object, such as a galaxy cluster, bends the light from a more distant object, like a quasar, creating multiple images of it. This effect is predicted by Einstein's theory of general relativity. When we observe the sky, we can distinguish between these rare gravitational lensing events and the vast majority of actual stars because lensing events are relatively rare and often involve detectable distortions and alignments that do not occur with the light from most nearby stars.