The complex ion $[Co(NH_3)_4Cl_2]^+$ corresponds to an octahedral complex of the type $[MA_4B_2]$ (where A is a neutral ligand $NH_3$ and B is an anionic ligand $Cl^-$).

1. Geometrical Isomerism: This type of complex exhibits geometrical isomerism because the two chloride ligands can be arranged in two different ways relative to the central metal ion:

• Cis-isomer: The two chloride ions are adjacent to each other (90° angle).
• Trans-isomer: The two chloride ions are opposite to each other (180° angle).

2. Different Properties: As noted in the NCERT text, these stereoisomers possess distinct physical properties, including colour. For the specific composition $CoCl_3 \cdot 4NH_3$ (which contains the $[Co(NH_3)_4Cl_2]^+$ ion), one isomer is violet (cis) and the other is green (trans) .

Therefore, the existence of different coloured complexes for this composition is due to geometrical isomerism .