A complex sentence is a sentence consisting of an independent clause and a subordinating clause. Or, to put it more simply, complex sentences involve more than just a straightforward noun + verb. Complex sentences include extra phrases added to a base sentence, but which cannot stand alone as a sentence. For example:
Published 4:00 am, Thursday, January 9, 1997. 1997-01-09 04:00:00 PDT Yosemite National Park -- Yosemite Valley is slowly drying out after what park rangers are calling the worst flood here in recorded history, leaving behind hundreds of upturned tent-cabins and acres of wrecked camping sites.
Yosemite fire near Half Dome forces airlifting of 85 people. Updated 7:28 am, Tuesday, September 9, 2014. In this Sunday, Sept. 7, 2014, photo provided by Michael Frye, a wildfire burns next to Half Dome in Yosemite National Park, Calif. As of Monday, the fire has burned through about four square miles.