Question

Solve:

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

• A. $\frac{1}{2}$
• B. $\frac{-1}{2}$
• C. $1$
• D. $-1$

Answer 1

Answer: (C)

$1$

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

Since, $|Z_1{Z}_2|=|Z_1||Z_2|$ and $|\frac{Z_1}{Z_2}|=\frac{|Z_1|}{|Z_2|}$

$=\sqrt{2}\cdot \frac{\sqrt{5}}{\sqrt{10}}=1$

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

Hence, option C.