Search any question & find its solution
Question:
Answered & Verified by Expert
If $\left|\begin{array}{ccc}6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i\end{array}\right|=x+i y$, where $i=\sqrt{-1}$, then what is $x$ equal to?
Options:
Solution:
2144 Upvotes
Verified Answer
The correct answer is:
0
$\left|\begin{array}{lcc}6 \mathrm{i} & -3 \mathrm{i} & 1 \\ 4 & 3 \mathrm{i} & -1 \\ 20 & 3 & \mathrm{i}\end{array}\right|$
$=6 \mathrm{i}\left[3 \mathrm{i}^{2}+3\right]+3 \mathrm{i}[4 \mathrm{i}+20]+1[12-60 \mathrm{i}]$
$=6 \mathrm{i}[-3+3]+12 \mathrm{i}^{2}+60 \mathrm{i}+12-60 \mathrm{i}$
$=-12+12=0=\mathrm{x}+\mathrm{iy}$
$\therefore \mathrm{x}=0$
$=6 \mathrm{i}\left[3 \mathrm{i}^{2}+3\right]+3 \mathrm{i}[4 \mathrm{i}+20]+1[12-60 \mathrm{i}]$
$=6 \mathrm{i}[-3+3]+12 \mathrm{i}^{2}+60 \mathrm{i}+12-60 \mathrm{i}$
$=-12+12=0=\mathrm{x}+\mathrm{iy}$
$\therefore \mathrm{x}=0$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.