Could someone please help me.
I was wondering if I have to use "that" in the following sentence:
I'm sure your friends will likely call you on your birthday.
Should there be a "that" between sure and friends?
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I'm sure your friends will likely call you on your birthday
In the sentence above, the phrase your friends will likely call you on your birthday is a Complement of the adjective sure. This type of clause is known as a content clause (as opposed to a relative clause, or a comparative clause).
Content clauses are often introduced by the subordinator that:
We only use that with declarative content clauses, not interrogative ones or exclamative ones:
When to use that in declarative content clauses
We always use that with a content clause when a content clause is the Subject of a sentence:
We also always use that if the content clause has been moved to a position before the Subject:
The sentence above is a version of I freely admit that I need help, where the Complement of admit has been moved to before the Subject, I.
We rarely use that if the content clause is the Complement of a preposition:
[There are a handful of very unusual prepositions such as notwithstanding which allow that.]
In nearly all other cases where the content clause is the Complement of a verb, noun, or adjective the word that is optional. It can be omitted or included as you see fit:
We are far more likely to omit that if it's the Complement of a simple high frequency verb, adjective or noun. We are also far less likely to omit that in formal writing:
In the Original Poster's sentence the content clause is the complement of the simple and high frequency adjective sure. The context is also not formal. The Original Poster can therefore freely omit that. The sentence will be both grammatical and appropriate.
Most of this information is available in: A Student's Introduction to English Grammar Huddleston & Pullum, 2005.