Question:
Write the value of $\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|$.
Solution:
$\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|$
Here,
$i^{2}=-1$
$\Rightarrow\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|=a^{2}+b^{2}+c^{2}+d^{2}$
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