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(B) Let $\Delta = \left| {\begin{array}{ccc} 1 + i & 1 - i & i \ 1 - i & i & 1 + i \ i & 1 + i & 1 - i \end{array}} ight|$.Applying $R_1 	o R_1 +

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$4 + 7i$

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(B) Let $\Delta = \left| {\begin{array}{ccc} 1 + i & 1 - i & i \ 1 - i & i & 1 + i \ i & 1 + i & 1 - i \end{array}} ight|$.Applying $R_1 	o R_1 + R_2 + R_3$:$\Delta = \left| {\begin{array}{ccc} 2 + i & 2 + i & 2 + i \ 1 - i & i & 1 + i \ i & 1 + i & 1 - i \end{array}} ight| = (2 + i) \left| {\begin{array}{ccc} 1 & 1 & 1 \ 1 - i & i & 1 + i \ i & 1 + i & 1 - i \end{array}} ight|$.Applying $C_2 	o C_2 - C_1$ and $C_3 	o C_3 - C_1$:$\Delta = (2 + i) \left| {\begin{array}{ccc} 1 & 0 & 0 \ 1 - i & 2i - 1 & 2i \ i & 1 & 1 - 2i \end{array}} ight|$.Expanding along $R_1$:$\Delta = (2 + i) [ (2i - 1)(1 - 2i) - (2i)(1) ]$$= (2 + i) [ (2i - 4i^2 - 1 + 2i) - 2i ]$$= (2 + i) [ (4i + 4 - 1) - 2i ]$$= (2 + i) [ 3 + 2i ]$$= 6 + 4i + 3i + 2i^2 = 6 + 7i - 2 = 4 + 7i$.

$\left| {\begin{array}{ccc} 1 + i & 1 - i & i \\ 1 - i & i & 1 + i \\ i & 1 + i & 1 - i \end{array}} \right| = $

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