Question

please answer this and faltu answers will be reported
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Answer 1

Step-by-step explanation:

We have,

$z = \bigg|(1 + i) \frac{(2 + i)}{(3 + i)} \bigg|$

$\implies \: z = \bigg|(1 + i) \frac{(2 + i)(3 - i)}{(3 + i)(3 - i)} \bigg|$

$\implies \: z = \bigg|(1 + i) \frac{(6 + 3i - 2i - {i}^{2}) }{(3)^{2} -( i)^{2} } \bigg|$

$\implies \: z = \bigg|(1 + i) \frac{(6 + i - ( - 1)) }{9 -( - 1) } \bigg|$

$\implies \: z = \bigg|(1 + i) \frac{(6 + i + 1) }{9 + 1 } \bigg|$

$\implies \: z = \bigg|(1 + i) \frac{(7+ i ) }{10 } \bigg|$

$\implies \: z = \frac{1}{10} \bigg|(1 + i) (7+ i ) \bigg|$

$\implies \: z = \frac{1}{10} | (7 + 7i + i + {(i)}^{2}) |$

$\implies \: z = \frac{1}{10} | 7 + 8i + (- 1) |$

$\implies \: z = \frac{1}{10} | 7 + 8i - 1 |$

$\implies \: z = \frac{1}{10} | 6+ 8i |$

$\implies \: z = \frac{1}{10} \times 2 \times | 3+ 4i |$

$\implies \: z = \frac{1}{5} | 3+ 4i |$

$\implies \: z = \frac{1}{5} \sqrt{ ( 3)^{2} + (4)^{2} }$

$\implies \: z = \frac{1}{5} \sqrt{ 9 + 16}$

$\implies \: z = \frac{1}{5} \sqrt{ 25}$

$\implies \: z = \frac{1}{5} \times 5$

$\implies \: z = 1$