Answer :
According to the given sentences, the complex sentence include option A: Edgar Allan Poe's stories, while they delight the imagination, also challenge one's intelligence.
What do you mean by Complex sentences?
A complex sentence is refers to as the sentence that include an independent clause with more than one subordinate clauses.
Moreover, a complex sentence is a clause that is missing either a subject or a predicate. We use these complex sentences in only that cases when we want to generate more data about something.
Adding to it, complex sentences often used because, since or until as a subordinating conjunctions. Likewise, in this case the option A is correct because it consists one independent clause and subordinate clauses. Rest all options like B,C and D are incorrect.
Therefore, correct option is A.
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