A coordination compound exhibits optical activity when it is chiral, meaning it is not superimposable on its mirror image and thus lacks symmetry. The complex \(\text{cis}-[\text{Co}(en)_2\text{Cl}_2]^+\) is optically active due to its asymmetric structure. Conversely, the \(\text{trans}-[\text{Co}(en)_2\text{Cl}_2]^+\) complex is optically inactive because it possesses symmetry; the opposing chloride ions are positioned opposite each other, resulting in a symmetrical configuration. Consequently, option (C) is the correct choice.