Examples
Example 1
I didn't prepare for my math test because my dog ate my calculator.
If your teacher believes that one, we have some swampland in Florida we'd like to sell him. First, let's break down this compound sentence. I didn't prepare for my math test is the independent clause. Because my dog ate my calculator is the dependent clause. The fact that it starts with because, which is a common subordinating conjunction, is a good clue that there's something complex going down here.
Example 2
My brutally honest friend Reese told me that my new jeans make my ears look enormous.
Reese: brutally honest since birth. We'll be brutally honest with you, too: in this complex sentence, the independent clause is My brutally honest friend Reese told me. That idea can stand on its own. The dependent clause is that my new jeans make my ears look enormous. That idea can't stand on its own; in order to make sense, it needs the rest of the sentence. Not that it makes much sense then, either.
Example 3
Some students listen better while doodling.
A recent study published in Applied Cognitive Psychology, our second favorite magazine after Highlights , found that doodlers actually remember more than people who don't scribble in the margins. If you study this sentence, you'll observe that it's a complex one: it has one dependent clause, Some students listen better, and one dependent clause, while doodling.