I'm happy to help with this.

This is a distinction that MGMAT draws in Vol 8, Ch. 11 of its series. I am not sure how useful a distinction this is.

First of all, a gerund is the "ing" form of a verb used as a noun. It can take any of the noun-roles in a sentence.

Singing is fun. (gerund as subject)
She hates waiting for the bus. (gerund phrase as direct object)
I will win the argument by turning the professor against her. (gerund phrase as an object of a prepositional phrase)

The first is just a single gerund by itself. The second two are gerund phrases --- MGMAT would call them "simple" gerund phrases.

According to their distinction, a "complex" gerund phrase would be one in which the gerund became even more "noun-like" because it is either preceded by an article or modified by an adjective.

The howling of a wolf in the distance is chilling at twilight.
Intemperate eating causes indigestion.

Both of those sentence contain gerund phrases that MGMAT would classify as "complex." Notice: complex is not necessarily long --- in the final sentence, the entire complex gerund phrase is compose of merely two words.

GMAT SC are simply littered with gerund phrases, all over the place, both simple & complex phrases. Again, as long as you recognize a gerund for what it is, it's not particularly clear to me that the distinction between simple & complex gerund phrases is going to help you much on GMAT SC.

Does all this make sense?

Mike
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Mike McGarry
Magoosh Test Prep