Evaluate x- 3 - i-5 3 - i-5 -3 - -2 i - -3 - -2 i

Solution x=(3+i√(5))(3 i√(5))(√(3)+√(2)i) (√(3) √(2)i) Apply a^2 b^2=(a+b)(a b) in numerator. x=9+52√(2)i=142√(2)i=7i√(2)i^2= 7√(2)i ...

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Complex Numbers

Evaluate x=...

Question

Evaluate $x = \frac{(3 + i \sqrt{5}) (3 - i \sqrt{5})}{(\sqrt{3} + \sqrt{2} i) - (\sqrt{3} - \sqrt{2} i)}$

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\frac{(3 + i \sqrt{5}) (3 - i \sqrt{5})}{(3 + \sqrt{2} i) (\sqrt{3} - i \sqrt{2})}

{(- 3 + 2 i)}^{2} - 3 (3 - i) (- 2 + 2 i)

i^{2} = - 1

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\frac{(3 + i \sqrt{5}) (3 - i \sqrt{5})}{(\sqrt{3} + \sqrt{2 i}) - (\sqrt{3} - i \sqrt{2})}

A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{- 1 + i \sqrt{3}}{2 i} & \frac{- 1 - i \sqrt{3}}{2 i} \frac{1 + i \sqrt{3}}{2 i} & \frac{1 - i \sqrt{3}}{2 i} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦, i = \sqrt{- i}

f (x) = x^{2} + 2

f (A)

z = ∣ ∣ ∣ ∣ \begin{matrix} 3 + 3 i & 5 - i & 7 - 3 i i & 2 i & - 3 i 3 - 2 i & 5 + i & 7 + 3 i \end{matrix} ∣ ∣ ∣ ∣

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