A complex sentence has an independent clause joined by one or more dependent clauses. A complex sentence always has a subordinator such as because, since, after, although, or when or a relative pronoun such as that, who, or which.

a. When he handed in his homework, he forgot to write his name on it.

b. The teacher gave back the homework after he noticed that the name was missing.

c. After they finished studying, Juan and Maria went to the movies to have some fun.

d. While I was reading "Wuthering heights", I heard a noise coming out of the kitchen :O

When a complex sentence begins with a subordinator such as sentences a comma is required at the end of the dependent clause. When the independent clause begins the sentence with subordinators in the middle as in sentences no comma is required. If a comma is placed before the subordinators in sentences t is wrong.

Adjective clauses

Finally, sentences containing adjective clauses (or dependent clauses) are also complex because they contain an independent clause and a dependent clause. The subjects, verbs, and subordinators are marked the same as in the previous sentences, and in these sentences, the independent clauses are also underlined.

a. The woman who (m) my mom talked to sell cosmetics

b. The book (that) Jonathan read is on the shelf.

c. The house which Abraham Lincoln was born in is still.

Adjective Clauses are studied in this site separately, but for now it is important to know that sentences containing adjective clauses are complex.

Original source http://www.eslbee.com :D