The term complex migraine syndrome is rarely used today. The terms complex migraine or complicated migraine can actually refer to a whole range of types of migraine, depending on who you talk to.
Back in 2011, reporter Serene Branson had a migraine attack on the air, which at first looked like it could be a stroke. This led to a lot of discussion about migraine, types of migraine, and migraine symptoms.
You can read about the various uses of the term complex migraine syndrome here.
Sometimes, the term is simply used to refer to various kinds of migraine with aura. In this video responding to the Branson news story, Dr. David Dodick of the Mayo Clinic discusses this type of migraine.