The correct option is B 1√(2) The value of |√(3) + i/(1 + i)(1 + √(3)i) | = |√(3) + i||1 + i||1 + √(3)i| = √(3 + 1)√(1 + 1)×√(1 + 3) = 22√( ...

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Property 1

|√3+i1+i1+√3i...

Question

$∣ ∣ ∣ ∣ \frac{\sqrt{3} + i}{(1 + i) (1 + \sqrt{3} i)} ∣ ∣ ∣ ∣ =$

1

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\sqrt{2}

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\frac{1}{2}

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\frac{1}{\sqrt{2}}

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Solution

The correct option is B $\frac{1}{\sqrt{2}}$
The value of $∣ ∣ ∣ ∣ \frac{\sqrt{3} + i}{(1 + i) (1 + \sqrt{3} i)} ∣ ∣ ∣ ∣$
$= \frac{| \sqrt{3} + i |}{| 1 + i | | 1 + \sqrt{3} i |} = \frac{\sqrt{3 + 1}}{\sqrt{1 + 1} \times \sqrt{1 + 3}}$
$= \frac{2}{2 \sqrt{2}}$
$= \frac{1}{\sqrt{2}}$

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