A complex sentence is a sentence with two or more of dependent sentences and independent sentences mixed together by subordinating conjunctions, such as "although," "after," "until," "while," or "when'".
For example: "Before the curtain rose, Nick came out and took a bow."
In this sentence, "before" is a subordinating conjunction. "Before the curtain rose" is a dependent sentence. With its subordinating conjunction, it joins the independent sentence by being smoothly contacted by its meaning. But without this independent sentence,"Nick came and took a bow", the dependent sentence cannot stay by itself. "Before the curtain rose" cannot stay by itself without an independent sentence joined together by adding a subordinating conjunction.