Hate to say it, but starch doesn't qualify as a simple sugar. Simple sugars are sucrose, glucose, fructose, galactose, maltose, etc. I'd say it stops at dimers. Starch is definitely a long polymer. Easier to digest into simple sugars than, say, chitin, but...
Don't hate to say when you're right. I should have been more specific and said simple carbs and starches, but I lump them together as they essentially end up doing the same thing within the body.