What word describes something that is impossible to placate?

The word that describes something that is impossible to placate is "implacable." This term specifically refers to a state or disposition that cannot be calmed, appeased, or satisfied, particularly in the context of anger or hostility. Therefore, someone who is implacable remains unforgiving or relentless, showing no signs of being able to be soothed or mollified.

In contrast, the other options convey different meanings that do not align with the concept of being unyielding or impossible to calm. "Gentle" suggests a mild or kind nature, "complacent" describes a state of self-satisfaction often unaware of potential dangers, and "amicable" refers to being friendly and agreeable. None of these terms capture the essence of being unable to placate, making "implacable" the most accurate choice.