Object or compliment?

[merkatron]

Hi

In the following clauses, how would you describe the relative clause's function? Is it functioning as part of the complement?

[I] [am] [confident] [that you long to hear from me].
S V COMP RELATIVE CLAUSE

If the sentence were

I hope that you arrive soon

instead, how would you then label the parts?

[Mister Micawber]

The 'that' clause in the first case is an adjective complement of 'confident'. The 'that' clause in the second instance is the direct object of 'hope'.

[I] [hope] [that you arrive soon].
S V DO

[merkatron]

Thanks, Mr M. Spelling's next on my list to improve!