Step 1: Understanding the Concept:
The oxidation state of the central metal equals the charge of the complex minus the total charge of the ligands.
Step 2: Calculation:
Let the oxidation state of Co be \(x\). Ammonia is a neutral ligand (charge 0).
\[ x + 6(0) = +3 \Rightarrow x = +3 \]
Step 3: Check the Other Options:
\(+5\) and \(+4\) would give a complex charge of \(+5\) or \(+4\), and \(+2\) would give \(2+\). Only \(+3\) matches the given \(3+\). So (C) is correct.
Final Answer:
Cobalt is in the +3 state, option (C).
\[ \boxed{\text{(C) } +3} \]