The direct and the prepositional indirect object may be simple and complex.
The complex object consists of two components, of which the second stands in predicate relation to the first. The two components form an indivisible unit and consequently must be regarded as one part of the sentence. The complex object can be non-prepositional and prepositional.
I observed Agnes turn pale. (Dickens)
Thus these two waited with impatience for the three years to be over. (Buck)
The first component of the complex object is a noun in the common case or in the possessive case, a personal pronoun in the objective case, or a possessive pronoun; the second is an infinitive, a participle, a gerund, seldom a noun, an adjective, a word denoting state, or a prepositional phrase.
He hated her to work in the boarding house. (Prichard)
On looking towards her again, I perceived her face clouded with embarrassment. (E. Bronte)
He could see the man and Great Beaver talking together. (London)
She thinks herself very clever.
As he spoke, he felt himself unusually on edge. (Lindsay)
NOTE: The group ‘object + objective predicative’ is very close to the complex object, but the connection between its two elements is not close enough to make them one part of the sentence; so while the complex object can nearly always be extended into an object Clause; the direct object with its objective predicative cannot.
E.g. He felt himself unusually on edge can be changed into He felt that he was unusually on edge, but They left him alone cannot be changed in the same way.
All the predicative constructions when used in the function of an object due to their structure form a complex object. Thus we have a complex object expressed by a participial construction, a gerundial construction, an Objective-with-the- Infinitive Construction and a for-to-Infinitive Construction.
Dick found himself walking in the direction of his friend Mike’s place. (Lindsay)
His new duties had kept him occupied. (Douglas)
My lady assures him of his being worth no complaint from her. (Dickens)
“Well,” said Soames, “I want you to come out to the Stores, with me, and after that we’ll go to the Park.” (Galsworthy)