Find the values of the following determinant- where i-1 1-3i i-2 -i-2 1-3i

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Definition of a Determinant

Find the valu...

Question

Find the values of the following determinant, where $i = \sqrt{- 1}$
$∣ ∣ ∣ \begin{matrix} 1 + 3 i & i - 2 - i - 2 & 1 - 3 i \end{matrix} ∣ ∣ ∣$

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Solution

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∣ ∣ ∣ \begin{matrix} 1 + 3 i & i - 2 - i - 2 & 1 - 3 i \end{matrix} ∣ ∣ ∣

i = \sqrt{- 1}

∣ ∣ ∣ \begin{matrix} 1 + 3 i & i - 2 - i - 2 & 1 - 3 i \end{matrix} ∣ ∣ ∣

i = \sqrt{- 1}

i = \sqrt{- 1} .

∣ ∣ ∣ \begin{matrix} 2 i & - 3 i i^{3} & {- 2 i}^{5} \end{matrix} ∣ ∣ ∣

∣ ∣ ∣ \begin{matrix} 1 + 3 i & i - 2 - i - 2 & 1 - 3 i \end{matrix} ∣ ∣ ∣

i = \sqrt{- 1}

∣ ∣ ∣ \begin{matrix} 2 i & - 3 i i^{3} & - 2 i^{5} \end{matrix} ∣ ∣ ∣

∣ ∣ ∣ \begin{matrix} 2 i & - 3 i i^{3} & - 2 i^{3} \end{matrix} ∣ ∣ ∣

i = \sqrt{- 1}

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