Question

The value of $\left|(1+i) \frac{(2+i)}{(3+i)}\right|$ is

(A) $-\frac{1}{2}$

(B) $\frac{1}{2}$

(C) 1

(D) -1

Answer 1

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

$=\sqrt{1+1} \times \frac{\sqrt{4+1}}{\sqrt{9+1}}=\sqrt{2} \times \frac{\sqrt{5}}{\sqrt{10}} $

$=\frac{\sqrt{10}}{\sqrt{10}}=1$

So, The correct option will be (C).