We have, (a + ib)(c + id)(e + if)(g + ih) = A + iB ∴ |(a + ib)(c + id)(e + if)(g + ih)| = |A + iB| ⇒ |a + ib||c + id||e + if||g + ih| = |A + iB| ⇒ $\sqrt{a^2+b^2} \sqrt{c^2+d^2}$ $\sqrt{e^2+f^2} \sqrt{g^2+h^2}$ = $\sqrt{A^2+B^2}$ ... (i) Squaring (i) both sides, we get, $(a^2+b^2)(c^2+d^2)$ $(e^2+f^2)(g^2+h^2)$ = $A^2+B^2$