Sir Arthur Conan Doyle presents Sherlock Holmes as a particularly fine detective. This starts right in the first chapter, when Sherlock makes deductions about a watch held by Watson. As Holmes says to Watson, "[his] mind rebels at stagnation", and it is this ever-busy mind which notices everything and makes him a great detective.

As in all his detective novels, Holmes’s approach to the mystery at hand in The Sign of Four shows him to be a man driven by rationality and common sense. For example, he makes the point that even if a scenario seems really unlikely, if he has ruled out every other possibility, then the one that seems improbable but has not been ruled out must in fact be the truth.

His powers of deduction seem to take on qualities of a sixth sense. He is not distracted by any personal issues, because he far prefers a line of cocaine to the idea of a wife or partner. It is apparent throughout that Holmes's powers of deduction and observation are second to none.

This novel showcases his single-minded focus on the task at hand and his refusal to allow social conventions, matters of the heart, or anything else stand between him and his getting to the bottom of this latest mystery.

The presentation of Sherlock Holmes in Arthur Conan Doyle's novel, The Sign of Four, is as a brilliant and cerebral man who can be extremely perceptive about small details but lacks self-awareness and emotional intelligence. Some readers might wish to argue that Holmes is represented as an example of someone with savant syndrome who might be on the autistic spectrum, albeit on the high-functioning end.

The opening of the novel shows Holmes as addicted to opioids. His unwillingness to follow the advice of Watson, a doctor by profession, is an example of his tendency to be self-centered and unwilling to take advice. Sherlock has a (deservedly) high opinion of himself, and despite his constant insistence on the need for pure rationality, he can show great kindness.

Holmes tends to be secretive, only revealing his discoveries when he has attained complete knowledge of a case—something that helps create suspense. He has an encyclopedic knowledge of matters relevant to his calling and a complete lack of interest in things he deems irrelevant to his interests or purposes.

How is Holmes a complex character in the first two chapters of The Sign of Four?

As mentioned in the other answer, we find out that Sherlock Holmes uses cocaine. Watson, as a doctor, is alarmed by this habit:

[It] involves increased tissue-change and may at last leave a permanent weakness. You know, too, what a black reaction comes upon you.

As Watson questions Holmes about it, we gain insights into Holmes's character. These insights reveal to readers how complex and unusual Holmes is. We learn, as Holmes asks Watson to look out the window, that he, Holmes, sees the world as an unsatisfying place. Humdrum reality does not appeal to him—people are dull—and he describes the world in terms that will find their echoes later in T.S. Eliot's "The Love Song of J. Alfred Prufrock":

A dreary, dismal, unprofitable world? See how the yellow fog swirls down the street and drifts across the duncolored houses. What could be more hopelessly prosaic and material?

Holmes explains to Watson that he takes cocaine as a form of escape from the tedium of not having an intricate problem to work on and also as a way to enhance reality. He calls cocaine "so transcendently stimulating and clarifying."

We learn too that Holmes perceives himself as set apart from other humans, calling himself the only person in the world doing the work he is doing. He is the "only unofficial consulting detective":

I am the last and highest court of appeal in detection.

He emphasizes over and over that mental stimulation and the life of the mind are all that makes life worth living to him. He even tells Watson that the problem Watson proposes to lay out for him will keep him from a second dose of cocaine.

We learn too that Holmes looks down on Watson's tendency to add a romantic, emotional, human element to his crime stories, stating that the emphasis should be on the science and the facts. He has no interest in the kind of romantic love that Watson feels for Miss Morstan.

From Watson's probing into his friend's cocaine habit, we learn that Holmes is world-weary, sets himself apart from the average person, and finds the mental stimulation of detection, along with other mental activities, all that makes life vital for him. Doyle does his best to reveal that Holmes is not an ordinary human being.

The Sign of Four is presented by Mary Morstan as a complex case. Holmes, being a complex man, is just the man to help solve it. In the first two chapters, Watson introduces various unusual character traits which will become familiar not just throughout the course of the book, but also in subsequent Sherlock Holmes adventures.

The story begins with Watson observing Holmes taking cocaine. He has been witnessing Holmes doing this three times a day for several months. Drug addiction was much more unusual in 19th-century England than it is today. The reason that Holmes gives for taking cocaine is also unusual; his mind "rebels at stagnation." Holmes needs to keep his mind active in order to solve such complex mysteries and regular injections of cocaine help him to do this. At the very least, he thinks it does.

Conan Doyle also allows us to marvel at Holmes's incredible powers of observation, as displayed in his brilliant deduction about the background history of the pocket watch belonging to Watson. Holmes correctly deduces that the watch once belonged to Watson's alcoholic brother from a simple examination of scratch marks and grooves.

It is here we see another character trait of Holmes that marks him out from the rest of humanity: a certain cold-bloodedness. When Holmes reveals the provenance of Watson's pocket watch, Watson is rather offended. Holmes means no offense; he is merely exercising his capacity for abstract logic to the utmost.

In chapter 2 we see this characteristic of Holmes when he is introduced to the comely Miss Morstan. After she presents Holmes with the facts of the case, Watson immediately observes how attractive the young lady is. Holmes, however, claims not to have noticed as he casually lights a pipe and sits back in his chair.

An exasperated Watson rebukes Holmes, describing him as an "automaton," and a "calculating machine"; indeed, there is something "positively inhuman" about him. Perhaps Watson is being a little harsh; however, we can still accept that Sherlock Holmes is no ordinary human being, as Conan Doyle makes perfectly clear in the first two chapters of The Sign of Four.

How does Arthur Conan Doyle present Sherlock Holmes in The Sign of Four?

Sherlock Holmes is the iconic detective who is depicted in The Sign of Four and many other works by Arthur Conan Doyle. He is brilliant but socially awkward and eccentric. Some recent writers have suggested that he shows certain characteristics of people on the autistic spectrum. When he gets bored, he uses drugs. He is a skilled violinist as well and an expert marksman who occasionally uses his walls for target practice. 

He is portrayed as a confirmed bachelor who appears to have little interest in romance or sexual relationships with neither men nor women. He can be a deeply loyal and caring friend, despite rarely showing or expressing emotions. He also has a strong sense of justice.

His main feature, though, is his intelligence and knowledge of many minute elements of forensic evidence that make him able to solve crimes, such as his ability to read tracks with great detail. He is also a master of deduction.