Persian Learner I'm sure I read an essay. = I'm sure [ that ] I read an essay. It complements 'sure'.
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Persian LearnerI'm sure I read an essay.= I'm sure [that] I read an essay.
Persian LearnerSo, it is a noun clause acting as an adjective complement, right?Correct, though you can say it's a complement of the verb phrase am sure. Nevertheless, I believe you have here a mix of two different systems of analysis.