How is moral complexity explored throughout the story?

Marlow understands and depicts Kurtz as a monster who rips the veil off any pretense that Europeans are colonizing to do "good" or bring civilization to the African natives. Kurtz moves from good intentions to becoming so overtaken with a lust for profit from ivory that he allows the natives to worship him as a god and treats them with extreme cruelty. He brings in more ivory than his peers but also upsets his higher-ups because of his unvarnished rapacity. In doing so, Kurtz—in being unabashedly about profit— exposes the hypocrisy of the Europeans' stated humanitarian reasons for being in Africa.
"All Europe contributed to the making of Kurtz," Marlow says. The moral complexity lies in that it is impossible to condemn Kurtz without condemning European imperialism as a whole—and that is what few among Marlow's peers want to do. It is easier to condemn an individual than an entire system, to see the "bad" person as aberrant—but this will not do. As many critics have pointed out, Kurtz is "hollow:" in many he is the reflection of other people's desires or projections. The moral dilemma then becomes: who is responsible for this man? How do we undo a system that he exposes as evil that yet makes life so much more comfortable for those far away in Europe? Today we can see imperialism as evil: a cognate for our times might be the evils of a carbon-based energy system that makes life comfortable to many but at what price?
Marlow can see the evil, but he can't deny that Kurtz was also other things than a greedy madman. He painted, so was an artist, and in some ways Marlow also admires him for his grandeur in refusing to put up a facade to hide what he really was.
At the end of the novel, Marlow refuses to tell Kurtz's fiancee the reality of what life was like in the Congo or Kurtz's true last words. Instead, he tells her Kurtz's last words were her name. He justifies this to the reader by stating that he can't live if there are no people in the world (women) who believe the illusion that imperialism—and hence European civilization— is good. This brings up another moral question: who, in the end, is worse: Kurtz, who exposes the insane greed and cruelty of the European system or Marlow, who covers it up and hence enables it?

The character of Kurtz embodies the moral complexity of the story. When Marlow first hears about Kurtz, Marlow thinks of him as superior, as embodying the values of Europe and the company. Marlow appears to be an asset to his trading company and someone who can supervise the extraction of an impressive amount of ivory.
However, as Marlow draws nearer to Kurtz, he discovers contradictions about him. For example, Marlow finds a piece of writing in which Kurtz, though eloquent and brilliant, recommends the extermination of "the brutes." Later, Marlow discovers that the native people at the Inner Station have been treating Kurtz as a kind of deity, a practice that Kurtz has encouraged. At the end of his life, Kurtz cries out, "The horror!" to characterize the way in which he and the other Europeans have treated the local people. As Marlow—and the reader—only meet Kurtz on his deathbed, Kurtz is a morally ambiguous character. The reader is not quite sure what to make of him, and this ambiguity, and the treatment of the local people in the hands of the Europeans—remain morally complex.

The famous phrase uttered by Kurtz as he is dying (“The horror! The horror!) remains one of literature’s great puzzles. The obscurity of this utterance is line with much of the novel’s insistence on obscurity, mystery and metaphysical questioning. Often, not even the questions being posed by the narrative are entirely clear. The answers are even less straight-forward.
As Marlow travels further up the Congo River, he finds a great deal of moral relativity (where one group may think a certain act is immoral another finds the same act to be entirely acceptable) and he finds that the central figure of the novel, Kurtz, is plagued by a sense of the flexibility of morality that might allow him to set himself up as a kind of god, above other men and free to act as he chooses without reprimand or question.
What is Kurtz’ project if not to achieve a new moral structure that makes him the authority on human life (and death)? Having ceased to do the work of the company, Kurtz is pursuing a greatness of a very peculiar order, one that is unclear in its motives and in its exact aims.
In a cultural context where a project of complete exploitation is underway, who can stand as a judge of morality? In a cultural context where foreign societies are interacting, who can arbitrate claims of right and wrong? These are among the many implied questions put forward in Heart of Darkness and they remain open questions to the end. No clear answers are provided by the narrative.