Evaluate the following determinants - a-ib c-id -c-id a-ib

a+ib #160; amp; c+id #160; c+id #160; amp; a ib #160; #160; =(a+ib)(a ib) (c+id)( c+id) (=a^2 (i^2 · b^2)) ( c^2+i^2 · d^ ...

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Definition of a Determinant

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Question

Evaluate the following determinants :
$∣ ∣ ∣ \begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix} ∣ ∣ ∣$

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lim x \to 0 {(\frac{a^{x} + b^{x} + c^{x} + d^{x}}{4})}^{1 / x} = 8,

∣ ∣ ∣ \begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix} ∣ ∣ ∣

A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]

a^{2} + b^{2} + c^{2} + d^{2} = 1

∣ ∣ ∣ \begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix} ∣ ∣ ∣ \times ∣ ∣ ∣ \begin{matrix} a - i β & γ - i δ - γ - i δ & a + i β \end{matrix} ∣ ∣ ∣

i = \sqrt{- 1}

∣ ∣ ∣ \begin{matrix} A - i B & C - i D - C - i D & A + i B \end{matrix} ∣ ∣ ∣

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