Question

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

Answer 1

Given,

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

$\left|\frac{z_1+z_2+1}{z_1-z_2+i}\right|$

$=\left|\frac{2-i+1+i+1}{2-i-1-i+i}\right|$

$=\left|\frac{4}{1-i}\right|$

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

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

$=\left|2(1+i)\right|$

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

$=\sqrt{8}$

$=2\sqrt{2}$