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. In this Sunday, Sept. 7, 2014, photo provided by Michael Frye, a wildfire burns next to Half Dome in Yosemite National Park, Calif.  (AP ...