If 6i -3i 1 4 3i -1 20 3 i -x-iy- where i-1- then what is x equal to-

The correct option is C 0 6i amp; 3i amp; 1 4 amp; 3i amp; 1 20 amp; 3 amp; i R _ 1 → R _ 1 + R _ 2 6i+4 ...

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Determinant

If 6i -3i...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + i y,$ where $i = \sqrt{- 1}$ , then what is x equal to?

3

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Solution

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∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + i y

∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + i y

I f ∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + y i

∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 2 & 3 & i 4 & 3 i & - 1 \end{matrix} ∣ ∣ ∣ ∣ = x + i y

{(\frac{3}{2} + i \frac{\sqrt{3}}{2})}^{100} = 3^{50} (x - i y)

i = \sqrt{- 1},

\frac{y}{x}

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