\[\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right) = {\left( {ac - bd} \right)^2} + {\left( {ad + bc} \right)^2} = {\left( {ac + bd} \right)^2} + {\left( {ad - bc} \right)^2}\]