The correct option is
C I live in a big apartment complex and it has many buildings.
A simple sentence has only one subject and predicate. It has a finite verb with a completed thought. A compound sentence has at least two parts (also referred to as a clause). Each part has its own subject and predicate and makes good sense by itself. Hence each clause is independent of the other and called the main clause or independent clause. The main clauses are connected using a co-ordinating conjunction (for, and, nor, but, or, yet, so).A complex sentence has at least one main clause (which is an independent clause) and one or more dependent clauses, connected using a subordinate conjunction. The dependent clause cannot stand by itself and make good sense. It depends on the main clause.
Option A: The clause, "The apartment has many buildings" is an independent clause. The clause, "in which I live" cannot stand independently and make good sense. It is a dependent clause. Hence, this is a complex sentence and this option is incorrect.
Option B: This sentence has only one clause i.e., "I live in a big apartment complex". It has only a single subject ("I") and predicate ("live in a big apartment complex"). The words, "with many buildings" is a phrase and not a clause. Hence, this is a simple sentence and this option is incorrect.
Option C: The two clauses viz (i) "I live in... complex" and (ii) "It has many buildings", can stand independently and make good sense. They are independent clausesconnected using the co-ordinating conjunction-"and". Hence, this is a compound sentence and this answer is correct.
Option D is incorrect as option C is the correct answer.