Step 1: Dimethylglyoxime and metal ion complexes.
Dimethylglyoxime is commonly used as a reagent to form colored complexes, particularly with metal ions such as Ni(II). The complex formed with Ni(II) is typically red.
Step 2: Analyzing each metal ion.
- Ni(II): Forms a red precipitate with dimethylglyoxime, indicating a positive test for nickel.
- Bi(III): Does not form a red precipitate with dimethylglyoxime.
- Zn(II): Forms a white precipitate with dimethylglyoxime, not a red one.
- Fe(II): Forms a light green precipitate with dimethylglyoxime, not a red one.
Step 3: Conclusion.
Only Ni(II) forms a red precipitate with dimethylglyoxime.
Final Answer:
\[
\boxed{\text{Ni(II)}}
\]