Question

the part of our brain which is used to imagine the dreams at night

Answer 1

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No one part of the brain "generates" dreams. Dreams are best viewed as a whole brain phenomenon -- or at least a "whole cerebral cortex" phenomenon.

The stages of sleep are controlled by an interconnected group of tiny nuclei (clusters of neurons) in the base of the brain and brain stem. Here is a picture of where they are located along with the feedback circuit controlling sleep and dreaming:

Rapid Eye Movement (REM) sleep, which is when most dreaming occurs, is "driven" from these nuclei. However the actual content of dreams comes from the  cerebral cortex as a whole using processes that may be similar to imagination.

In normal perception, information from the senses is organized in a "bottom-up" fashion to form a model of the world. In imagination and probably dreaming, the process works in reverse: a high-level (and possibly arbitrary) model of the world is transformed in a "top-down" fashion into perceptual details.

The dominant theory in neuroscience is that the perceptual experiences of dreaming are a side-effect of a memory consolidation process occurring during sleep. The idea is that the brain reorganizes memories by playing back encoded aspects of them and recoding them into a more efficient and useful form for long-term storage and behavior control.

Answer 2

The whole brain is active during dreams, from the brain stem to the cortex. Most dreams occur during REM (rapid eye movement) sleep. This is part of the sleep-wake cycle and is controlled by the reticular activating system whose circuits run from the brain stem through the thalamus to the cortex.