Explanation:
The given complex contains K, Pt(IV), and Cl-. The complex is said to be 100% ionized, meaning that all of the complex ions dissociate into their constituent ions when dissolved in a solvent. The dissociation of ions in a solution is quantitatively measured by the van't Hoff factor, denoted by i.

Van't Hoff Factor (i):
The van't Hoff factor (i) is the ratio of the moles of particles formed when a substance is dissolved in a solvent to the moles of formula units dissolved. It is used to determine the extent to which a substance dissociates or ionizes in a solution.

Given Information:
In this case, the given complex is 100% ionized, and the van't Hoff factor (i) is given as 3.

Determination of Complex:
To determine the complex, we need to examine the ions present in the solution and their possible combinations.

The complex contains K, Pt(IV), and Cl-. The charge on K is +1, the charge on Pt(IV) is +4, and the charge on Cl- is -1.

Possible Combinations:
Using the given ions, we can form the following combinations:

1. K[PtCl3]: This complex would have a van't Hoff factor of 2, as it would dissociate into K+ and [PtCl3]- ions.

2. K2[PtCl4]: This complex would have a van't Hoff factor of 3, as it would dissociate into 2K+ and [PtCl4]2- ions.

3. K3[PtCl5]: This complex would have a van't Hoff factor of 4, as it would dissociate into 3K+ and [PtCl5]3- ions.

4. K2[PtCl6]: This complex would have a van't Hoff factor of 3, as it would dissociate into 2K+ and [PtCl6]2- ions.

Selection of Complex:
The given van't Hoff factor is 3, which eliminates the possibilities of K[PtCl3] and K3[PtCl5] complexes, as they have van't Hoff factors of 2 and 4, respectively.

Therefore, the correct complex is K2[PtCl6], as it has a van't Hoff factor of 3, which matches the given information.

Conclusion:
The correct complex is K2[PtCl6], option (b).