(d)$\left| {\,\begin{array}{*{20}{c}}{6i\,\,\,}&{ – 3i\,\,\,}&{\,\,1}\\{4\,\,}&{3i}&{ – 1}\\{20\,}&3&{\,\,i}\end{array}\,} \right|$=$x + iy$

$⇒  \left| {\,\begin{array}{*{20}{c}}{6i + 4\,\,\,\,}&{0\,\,\,\,}&{\,\,0}\\{4\,\,\,}&{3i\,\,\,\,}&{ – 1}\\{20\,\,\,}&{3\,\,\,\,}&{\,\,i}\end{array}\,} \right| = x + iy$ $[{R_1} \to {R_1} + {R_2}]$

$⇒  (6i + 4)\,(3{i^2} + 3)$= $x + iy$ 

$⇒(6i + 4)\,( – 3 + 3) = x + iy$

  $⇒ x + iy = 0\,\, = 0 + i.0$ 

$ ⇒  (x,\,y)\, = (0,\,0)$.