The correct option is D 5 = | (3+i)(2 i)1+i| =|6 3i+2i+11+i| =|7 i1+i| =|(7 i)(1 i)2| =|7 7i i 12| =|6 8i2| =|3 4i| ...

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Properties of Modulus

| 3+i2-i 1+i ...

Question

$∣ ∣ ∣ \frac{(3 + i) (2 - i)}{1 + i} ∣ ∣ ∣ =$

\sqrt{5}

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5 \sqrt{2}

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\sqrt{10}

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5

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Solution

The correct option is D $5$
$= | \frac{(3 + i) (2 - i)}{1 + i} |$
$= | \frac{6 - 3 i + 2 i + 1}{1 + i} |$
$= | \frac{7 - i}{1 + i} |$
$= | \frac{(7 - i) (1 - i)}{2} |$
$= | \frac{7 - 7 i - i - 1}{2} |$
$= | \frac{6 - 8 i}{2} |$
$= | 3 - 4 i |$
$= \sqrt{3^{2} + 4^{2}}$
$= \sqrt{25}$
$= 5$

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