Step 1: Write the formula of the complex.
Hexammine cobalt(III) chloride has the formula \([\text{Co}(\text{NH}_3)_6]\text{Cl}_3\).
Step 2: Determine coordination number.
Six ammonia ligands are attached to cobalt, so coordination number is 6, not 9.
Step 3: Determine oxidation state.
Ammonia is a neutral ligand and three chloride ions are present outside the coordination sphere. Hence, oxidation state of cobalt is \(+3\).
Step 4: Nature of complex.
All ligands are same (homoleptic) and the complex ion is cationic, not anionic.
Step 5: Conclusion.
Thus, the correct statement is that the oxidation state of cobalt is \(+3\).