A complex sentence is made up of one main clause and at least one subordinate clause.
Without the underlined parts, the above sentences still express a complete idea. These are the main clauses of the sentences.
The underlined parts of the above sentences do not express a complete thought and appear incomplete. They are dependent on the main clause. These are called subordinate clauses and are joined to the main clause by subordinating conjunctions and relative pronouns.
Subordinating Conjunctions: when, that, while, where, because, before, after, why, for, as, if, until, whether, since, though, unless, and than
Relative Pronouns: who, where, whose, whom, which, and that