He shows what? The dependent clause that the world is a complicated place serves as an object. It is what he shows. There is no reason in this case to separate the verb from its object.

Correction: He shows that the world is a complicated place.

Consider a slightly different example. Alternate example: He shows, and showing isn't easy, that the world is a complicated place. In this case the commas are appropriate because there is now a phrase between the verb and the object. The first comma tells the reader that we are leaving the main sentence for awhile, the second comma says that we have returned to the main sentence.

Check the following resources for useful practice material: 1) Guide to Grammar and Writing, 2) Colleen Hildebrand's UCI Correction Symbols with hyperlinks.

For more on punctuation, visit the LARC Electronic Writing Center Grammar Checklist.