Step 1: Assign charges of known species.
- Potassium (K) has an oxidation state of \( +1 \).
- Carbonyl (CO) is a neutral ligand, so each CO contributes \( 0 \) charge.
Step 2: Write the overall charge balance equation.
Let the oxidation number of cobalt be \( x \). The complex ion is \([Co(CO)_4]^-\), since K is outside with \( +1 \).
\[
x + (4 \times 0) = -1
\]
Step 3: Solve for \( x \).
\[
x = -1
\]
Thus, the oxidation number of cobalt in \( K[Co(CO)_4] \) is \( -1 \).