Find the value of- 3 - -2i - 3-2i 5 - 2i 5 - 2i

Given, 3+√(2)i (3√(2)i)(5+2i)(5 2i) =3+√(2)i 3√(2)i(5+2i)(5 2i) =3 2√(2)i(5+2i)(5 2i) =3 2√(2)i29 =329 2√(2)29i ...

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Algebra of Complex Numbers

Find the valu...

Question

Find the value of:
$\frac{3 + \sqrt{2 i} - (3 \sqrt{2 i})}{(5 + 2 i) (5 - 2 i)}$

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Solution

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(5 + 2 i) (5 - 2 i)

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^{5} \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} ∣ ∣ ∣

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

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