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.
Simpson explores the history and issues surrounding the Hetch Hetchy dam at Yosemite National Park, which was built to supply San Francisco with water and power even though the site was already protected within the national park.