Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
$\left|\begin{array}{ccc}1+i & 1-i & i \\ 1-i & i & 1+i \\ i & 1+i & 1-i\end{array}\right|=$
MathematicsDeterminantsJEE Main
Options:
  • A $-4-7 i$
  • B $4+7 i$
  • C $3+7 i$
  • D $7+4 i$
Solution:
2788 Upvotes Verified Answer
The correct answer is: $4+7 i$
$\begin{aligned} & \Delta=(2+i)\left|\begin{array}{ccc}1 & 1 & i \\ 1 & 1+2 i & 1+i \\ 1 & 2 & 1-i\end{array}\right| \\ & =(2+i)\left|\begin{array}{ccc}0 & -2 i & -1 \\ 0 & -1+2 i & 2 i \\ 1 & 2 & 1-i\end{array}\right| \text { by } \begin{array}{l}R_1 \rightarrow R_1-R_2 \\ R_2 \rightarrow R_2-R_3\end{array} \\ & =(2+i)\left\{-4 i^2+(-1+2 i)\right\}=(2+i)(4-1+2 i) \\ & =(2+i)(3+2 i)=4+7 i .\end{aligned}$

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.