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.
In Yosemite Valley, Half Dome Village (formerly Curry Village), Yosemite Valley Lodge (formerly Yosemite Lodge), and The Majestic Yosemite Hotel (formerly The Ahwahnee), and Housekeeping Camp are open. Outside of Yosemite Valley, the Big Trees Lodge (formerly Wawona Hotel) is open. Tuolumne Meadows Lodge is open.