modifiers - Does the sentence "I am surprised" have the pattern (S+V+C)?

I am confused about this sentence pattern (S+V+C):

1. 
   

   I am surprised [ to see you ].

   
   


2. 
   

   I am surprised [ at how many have never heard of it ].

   
   


3. 
   
   

   I am surprised [ by his response ].

   
   


4. 
   

   I am surprised [ that some people study the past ].

   
   

I think that the sentence "I am surprised" has the sentence pattern "Subject + Verb + Complement".

So the phrases following the complement should be adverb phrases, because they modify the complement (surprised), right?

But the sentence "that some people study the past" is a nominal clause. It should be unable to modify the complement (surprised).

So why are these following phrases able to modify the complement?

• to see you


• at how many have never heard of it


• by his response


• that some people study the past