Answer:
The phrase "Juan was writing his paper" is a Noun Phrase, in addition to being an independent clause. The phrase "while his sleeping dog napped by his feet" is a Conjunctional Phrase, in addition to being a dependent clause. The two sentences together form a complex sentence.
Step-by-step explanation:
A complete sentence is one that has a dependent clause and an independent clause. Dependent clauses are those that cannot emit meaning alone and need to be complemented by the independent clause, which is the one that has meaning alone.
In the sentence shown above, "Juan was writing his paper" is the independent clause and can also be considered a Noun Phrase, which are phrases that are established around a single noun that is the subject of the sentence, in this case, the noun is the word "Juan."
The "while his sleeping dog napped by his feet" clause is a dependent clause and is a Conjunctional Phrase that are phrases that always start with a conjunction. The word "while" is a subordinate conjunction, as it is able to link a dependent clause to an independent clause.