Unnecessary Comma in a Complex Sentence

Complex sentences are sentences which have two clauses. There can be two independent clauses (each having a subject and predicate), or an independent clause and a dependent clause (missing a subject or predicate). Generally, if the dependent clause comes second, a comma is not used before the dependent clause. Frequently, but not always, a conjunction will begin the dependent clause.

I need to do the shopping, because there is nothing to eat in the house.

The second clause, because there is nothing to eat in the house, is dependent; there is no need to use a comma between the two clauses.

It makes no sense to study Advanced Pure Math, if the student will not use the math at a later date.

I’ll put the book down and sleep, when I can no longer keep my eyes open.

We don’t need a comma in these sentences, either.

Exception: If the sentence is too long or confusing without a comma, one may be used for purposes of clarity.

In the background of the painting there are a boat, a river, and a sunset, which attract the viewer’s attention.

Here, a comma is used before the dependent clause because otherwise the reader may think only the sunset attracts the viewer’s attention.