$∣ ∣ ∣ ∣ \begin{matrix} 1 + i & 1 - i & i 1 - i & i & 1 + i i & 1 + i & 1 - i \end{matrix} ∣ ∣ ∣ ∣ =$

-4-7i

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4+7i

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3+7i

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7+4i

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Solution

The correct option is B 4+7i
$Δ = (2 + i) ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & i 1 & 1 + 2 i & 1 + i 1 & 2 & 1 - i \end{matrix} ∣ ∣ ∣ ∣ = (2 + i) ∣ ∣ ∣ ∣ \begin{matrix} 0 & - 2 i & - 1 0 & - 1 + 2 i & 2 i 1 & 2 & 1 - i \end{matrix} ∣ ∣ ∣ ∣ b y \begin{matrix} R_{1} \to R_{1} - R_{2} R_{2} \to R_{2} - R_{3} \end{matrix} = (2 + i) {- 4 i^{2} + (- 1 + 2 i)} = (2 + i) (4 - 1 + 2 i) = (2 + i) (3 + 2 i) = 4 + 7 i .$

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