A complex sentence is made from an independent clause and a dependent clause joined together.

Some examples:

After I came home, I made dinner.

(dependent clause: "After I came home")

(indpendent clause: I made dinner)

We visited the museum before it closed.

(dependent clause: before it closed.)

(independent clause: We visited the museum)

Complex sentences are often formed by putting these words at the beginning of the dependent clause: as, as if, before, after, because, though, even though, while, when, whenever, if, during, as soon as, as long as, since, until, unless, where, and wherever. These words are called subordinating conjunctions.

Because the bridge wasn't properly maintained by the government, it fell down.

indpendent clause: it fell down

dependent clause: because the bridge wasn't properly maintained by the government

He'll be able to maintain a healthy weight if he keeps exercising.