A complex sentence is a sentence that has one independent clause and one or more dependent clauses. And also, the use of subordinating conjunction also signifies a complex sentence.
In the given sentence, the subordinating conjunction is "since". This makes the first part of the sentence the dependent clause. And the second part of the sentence is an independent clause as it can be taken as a full sentence on its own. And with that, the whole sentence contains a dependent clause with a subordinating conjunction and an independent clause, which makes it a complex sentence.
Madison believed that a republic would be better than a pure democracy for a large and populous nation. In at least 100 words, describe how Madison defined pure democracy. Then provide one or two examples of situations in which a pure democracy could be the best type of government.
Your purpose for writing the essay might be to persuade the reader to watch that particular TV show. (As for the questions below, I think you have to answer those yourself based on the TV show you've chosen.)