Question

(1+i) (2 +і) /(3 +і) find modulus​

Answer 1

Answer:

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

$\: \: \: \: = \frac{ |1 + i| |2 + i| }{ \sqrt{3 {}^{2} - i {}^{2} } }$

$\: \: \: \: = \frac{( \sqrt{1 {}^{2} - i {}^{2}) } ( \sqrt{2 {}^{2} - i {}^{2} } }{ \sqrt{9 + 1} } \: \: \: \: \: since \: \: - i {}^{2} = + 1$

$\: \: \: \: = \frac{ ( \sqrt{1 + 1)} ( \sqrt{4 + 1} )}{ \sqrt{10} }$

$\: \: \: \: = \frac{( \sqrt{2)} ( \sqrt{5} )}{ \sqrt{10} }$

$\: \: \: \: = \frac{ \sqrt{10} }{ \sqrt{10} }$

$\: \: \: \: = 1$