Step 1: Understand Optical Activity.
A compound exhibits optical activity if it lacks a plane of symmetry and is chiral. This means that the molecule should not superimpose on its mirror image. Coordination compounds with square planar or octahedral geometry can exhibit optical activity if they are unsymmetrical.
Step 2: Analyze the given complexes.
- Option (A): cis-\([ \text{PtCl}_2 (\text{en})_2 ]^{2+}\) is optically active because the two \( \text{en} \) ligands are not symmetrically placed and give rise to chirality.
- Option (B): \([ \text{Co}(\text{en})_3 ]^{3+}\) is optically active because the complex has no symmetry and is chiral.
- Option (C): trans-\([ \text{CoCl}_2 (\text{en})_2 ]^{+}\) is not optically active. The trans configuration leads to symmetry, making the complex achiral.
- Option (D): cis-\([ \text{CoCl}_2 (\text{en})_2 ]^{+}\) is optically active because the complex is not symmetrical and is chiral.
Step 3: Conclusion.
The complex in option (C), trans-\([ \text{CoCl}_2 (\text{en})_2 ]^{+}\), is achiral and does not exhibit optical activity. Therefore, the correct answer is option (C).