A complex sentence has two parts: a subordinate clause and an independent clause.
The subordinate clause always begins with a subordinating conjunction.
Here are two subordinating conjunctions that begin subordinate clauses: before and after.
Anytime you begin a sentence with the word before, you are writing a subordinate clause.
Before I mow the lawn
This is a subordinate clause beginning with the subordinating conjunction before.
It doesn’t make sense. A subordinate clause needs an independent clause attached to it in order to make sense.
Before I mow the lawn, I want to rake up the leaves.
Before I mow the lawn, I need to go buy gas.
Now these complex sentences make sense. We put a comma after the subordinate clause and then added an independent clause.
Here are more complex sentences beginning with the subordinating conjunction before:
Before we start play practice, I need to find the microphone.
Before I go to bed, I need to let the dog out one more time.
The word after is also a subordinating conjunction.
After we eat dinner.
This subordinate clause makes no sense by itself. We need to add a comma and an independent clause.
After we eat dinner, I will clean up the kitchen.
After we eat dinner, you can take out the trash.
Here are more examples of complex sentences beginning with the subordinating conjunction after:
After I read this book, I want to watch the movie.
After I wash the windows, it always rains.
Anytime you begin a sentence with before or after, you are writing a subordinate clause. You must put a comma after the subordinate clause and then add an independent clause in order to write a complete complex sentence.