Question

Find the values of the following determinants
$\left|\begin{array}{cc}1+3i& i-2\\ -i-2& 1-3i\end{array}\right|$
where $i=\sqrt{-1}$.

Answer 1

$\left|\begin{array}{cc}1+3i& i-2\\ -i-2& 1-3i\end{array}\right|$

$=(1+3i)(1-3i)-(2-2)(-i-2)$

$=(1-9i^2)-(-1^2-2i+2i+4)$

$=(1+9)-(1+4)$

$=10-5$

$=5$.