Unless there was good reason to think the complexity is a necessary condition for intelligence it wouldn’t be clear if that complexity is a result of evolving from a common ancestor. I don’t see any reason to think complexity is a necessary condition for intelligence since the concept of an intelligent immaterial mind not made of parts is coherent.

So, your response seems to be that complexity is not a necessary condition for intelligence because a simple intelligent immaterial mind is coherent. In response, an undesigned complex universe also seems logically coherent.

You could claim that observations contradict that (i.e., in our experience, whatever is complex is designed), but in our experience whatever is intelligent is complex -- induction supports both propositions.

Now, you could reply that just because "intelligent human life forms" are complex, that doesn't mean the intelligent designer of our world must be complex -- after all, it could be a simple immaterial mind. And in response I say that just because we observe on earth that complex artifacts always come from intelligent designers, that doesn't mean the entire universe is designed -- after all, it is possible it has some unknown property that allows it to be complex and yet undesigned.