Step 1: The complex ion \( [{Cu(NH}_3)_4]^{2+} \) consists of a central copper ion surrounded by four ammonia ligands. The copper ion in this case is in the \( {d}^9 \) configuration.
Step 2: For a \( {d}^9 \) metal ion, the geometry of the complex is typically square planar due to the electronic configuration and ligand field.
Step 3: Therefore, the shape of \( [{Cu(NH}_3)_4]^{2+} \) is square planar.