Which of the following complexes contains the transition metal cobalt in the +3 oxidation state?

The correct answer is based on the oxidation states of cobalt in the given complexes. In the complex [Co(NH₃)₆]³⁺, cobalt is indeed in the +3 oxidation state. The ammonia (NH₃) ligands are neutral, meaning they do not contribute to the charge of the complex. Therefore, for the entire complex, which has an overall charge of +3, the cobalt must also be in the +3 state to maintain this charge.

This contrasts with the first option, where cobalt is in the +2 oxidation state. The second choice contains both ammonia and chloride ligands and is positively charged as a whole; thus, cobalt is in the +3 state here as well. The fourth choice, [CoCl₃]²⁻, indicates cobalt would have to be in an oxidation state that would balance the charges of the three chloride ions (each having a -1 charge). This would not give cobalt a +3 state in a neutral or positively charged complex.

Therefore, the identification of [Co(NH₃)₆]³⁺ as having cobalt in the +3 oxidation state accurately reflects the nature of the ligands and the overall charge of the complex.