Step 1: In the complex \([Ti(H_2O)_6]^{3+}\), the titanium ion is in the +3 oxidation state with electronic configuration: \[ Ti^{3+}: [Ar]\,3d^1 \] Step 2: The presence of one unpaired electron in the 3d orbital allows for electronic transitions between \( t_{2g} \) and \( e_g \) levels when light is absorbed. Step 3: This \( d{-}d \) transition is responsible for the colour observed in the complex.