For foreign language learners, To find the difference between Object and Complement in one case which is going to discuss below is difficult. Here, I'm trying to discuss the lesson.

Object is something done by subject. It refers to an action (done by subject). Complement is to give more information about the verb. There has been a gap between the two (actually) differences.

Understand What Transitive and Intransitive Verbs
For example:

1. Tina goes home late every day.
2. Tina is drawing a beautiful painting.

In (1), the verb /goes/ is intransitive verb. Intransitive verb is a kind of verb which can not be added an object after it. To make sure whether the statement above is right or not, see this following example:

Active Voice > I need a book.
Passive Voice >  A book is needed by me.

In the active voice. the verb /need/ has an object /a book/. This verb is in Transitive verb and when it is changed into Passive voice, /the book/ will be the subject and /I/ which becomes the subject will turn to be an object. This proves that Transitive Verb can be added an object. Transitive Verb then has an object and can be changed into Passive and it is different of Intransitive verb.

Now try to change this sentence (Active voice) into Passive voice:
I live in Indonesia.

In (2), the verb /drawing/ is a Transitive verb. It has an object (A beautiful painting). So, it can be changed into passive voice, namely, A beautiful painting is being drawn by Tina.

Complement is used to give more information to the verb.

For example:

I went with him last night.

/with him/ is not an object. It is because the verb /went/ is in Intransitive Verb. Here, /with him/ is the complement. 

Compare this follows!

I went last night.
I went with him.
I went with him last night.

Complement can be like an object and we will find that there is a preposition which is being used in /with him/. Therefore, It is impossible for us to say: "I went him last night" (/him/ without /with/).

We also can see that complement is also used in Nominal Pattern.
For example:

I am happy.
She is lonely.
We are students of SMA 1 Negeri Bukit Kemuning.
Rita is a pretty dancer.
He was at home.

All the italic words or expressions above are the complement. The function of the verb "be" there is the same as Intransitive verb.

Compare and find the answer!

I am tired.
I get tired.

/am/ and /get/ have the same functions. Those give us information about the subject. Therefore, /tired/ is the complement. We also call the pattern as Linking-Verb.

see more Transitive and Intransitive Verb in this blog.