Explanation:

The existence of two different colored complexes with the composition of [Co(NH3)4 Cl2] is due to geometrical isomerism.

Geometrical isomerism:
Geometrical isomerism is a type of stereoisomerism that arises due to the different spatial arrangements of ligands around a central metal ion in a coordination complex. This type of isomerism occurs when there is restricted rotation around a metal-ligand bond, resulting in different possible arrangements of ligands.

In the case of [Co(NH3)4 Cl2], the central metal ion is cobalt (Co) and it is surrounded by four ammine (NH3) ligands and two chloride (Cl) ligands. Here, the cobalt ion is in the +3 oxidation state.

Formation of isomers:
In this complex, the two chloride ligands can occupy either adjacent or opposite positions around the cobalt ion.

- If the chloride ligands are adjacent to each other, it is called a cis isomer.
- If the chloride ligands are opposite to each other, it is called a trans isomer.

Reason for different colors:
The two different colored complexes with the composition of [Co(NH3)4 Cl2] arise due to the presence of these cis and trans isomers.

- The cis isomer appears green in color because the arrangement of ligands results in a particular electronic transition that absorbs light in the red region of the visible spectrum, giving rise to the complementary green color.
- The trans isomer appears purple in color because the arrangement of ligands results in a different electronic transition that absorbs light in the yellow region of the visible spectrum, giving rise to the complementary purple color.

Conclusion:
Therefore, the existence of two different colored complexes with the composition of [Co(NH3)4 Cl2] is due to geometrical isomerism, which arises from the different spatial arrangements of the ligands around the cobalt ion.