Question

If $z_1=2-i$ and $z_2=1+i$, then $\left|\frac{z_1+z_2+1}{z_1-z_2+i}\right|$ is

• A. $2$
• B. $2\sqrt{2}$
• C. $3$
• D. $\sqrt{3}$
• E. $1$

Answer 1

Answer: (B)

$2\sqrt{2}$

Given, $z_1=2-i$ and $z_2=1+i$

Then, $\left|\frac{z_1+z_2+1}{z_1-z_2+i}\right|=\left|\frac{2-i+1+i+1}{2-i-1-i+i}\right|$

$=|\frac{4}{(1-i)}\times \frac{(1+i)}{(1+i)}|$

$=\left|\frac{4(1+i)}{2}\right|$

$=|2+2i|$

$=\sqrt{(2{)}^2+(2{)}^2}$

$=\sqrt{8}=2\sqrt{2}$