Question

Evaluate:

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

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

Answer 1

The correct option is C $1$

$i^2=-1$

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

$|\frac{1+3i}{(3+i)}\times \frac{(3-i)}{(3-i)}|=\left|\frac{3-i+9i-3i^2}{9-i^2}\right|=\left|\frac{6+8i}{10}\right|$

$\Rightarrow |0.6+0.8i|=\sqrt{(0.6{)}^2+(0.8{)}^2}=1$