Complex sentence
A complex sentence is a sentence that has at least one dependent clause—for example:
So it isn’t surprising that his song about mass-murderer Charles Whitman is gloriously irreverent and wildly offensive. [AV Club]
Independent clause: So it isn’t surprising
Dependent clause: that his song about mass-murderer Charles Whitman is gloriously irreverent and wildly offensive
It begins when young sisters Scarlett and Rosie March are attacked in their home by a Fenris . . . [Novel Novice]
Independent clause: It begins
Dependent clause: when young sisters Scarlett and Rosie March are attacked in their home by a Fenris
The fat man seated in front of Patricia Marx, I learn, has “a bad case of sleep apnea.” [The Paris Review Blog]
Independent clause: The fat man . . . has “a bad case of sleep apnea.”
Dependent clauses: 1) [who is] seated in front of Patricia Marx; 2) I learn
A complex sentence that is also a compound sentence (one with two or more independent clauses) becomes a complex-compound sentence.