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Complex Numbers and Quadratic Equations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations1 Mark
Question
Find $\Big|(1+\text{i})\frac{(2+\text{i})}{(3+\text{i})}\Big|$
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Answer

$\Big|(1+\text{i})\frac{(2+\text{i})}{(3+\text{i})}\Big|=|1+\text{i}|\frac{|2+\text{i}|}{|3+\text{i}|}$
$=\sqrt{1^2+1^2}\frac{\sqrt{2^2+1^2}}{\sqrt{3^2+1^2}}$
$=\sqrt{2}\frac{\sqrt{5}}{\sqrt{10}}=1$

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