Step 1: Understanding the Question:
We must write the structural formulas from the given IUPAC names of several coordination compounds and identify the one that physically features a complex, negatively charged coordination sphere (a complex anion).
Step 2: Detailed Explanation:
Let's decode the IUPAC nomenclature for each compound to establish its cationic and anionic parts:
(b) Triamminetrinitrocobalt (III): Formula is $[\text{Co}(\text{NH}_3)_3(\text{NO}_2)_3]$. This is a completely neutral molecular complex. It has neither a simple cation nor a simple anion.
(c) Pentaammineaquacobalt (III) iodide: Formula is $[\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]\text{I}_3$. (Note: Assuming Co(III) is standard, though option says II. If II, $[\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]\text{I}_2$). In either case, the complex sphere is positively charged ($2+$ or $3+$), so it is a complex cation. The anion is simple (iodide, $\text{I}^-$).
(d) Hexaamminecobalt (III) chloride: Formula is $[\text{Co}(\text{NH}_3)_6]\text{Cl}_3$. The complex sphere is positively charged ($3+$), making it a complex cation. The anion is simple (chloride, $\text{Cl}^-$).
(a) Sodium hexanitrocobaltate (III): Formula is $\text{Na}_3[\text{Co}(\text{NO}_2)_6]$.
Here, the cation is simple (Sodium, $\text{Na}^+$).
The coordination sphere contains the cobalt metal and six negatively charged nitro ligands. The total charge of the sphere is $(+3) + 6(-1) = -3$.
Because the coordination sphere carries a negative charge, it is a complex anion ($[\text{Co}(\text{NO}_2)_6]^{3-}$). This is also reflected in the nomenclature suffix "-ate" added to the metal (cobaltate), which exclusively denotes a complex anion.
Step 3: Final Answer:
The compound containing a complex anion is Sodium hexanitrocobaltate (III), matching option (a).