If for complex numbers $z_1$ and  $z_2,$ $arg(z_1/z_2)=0,$then $|z_1-z_2|$ is equal to

We have $|z_1-z_2{|}^2$ 

$=|z_1{|}^2+|z_2{|}^2-2\left|z_1\right|\left|z_2\right|\cos ({\theta }_1-{\theta }_2)$

where ${\theta }_1=arg\left(z_1\right)$ and ${\theta }_2=arg\left(z_2\right)$

Since  $arg{z}_1-arg{z}_2=0$

\ $|z_1-z_2{|}^2=|z_1{|}^2+|z_2{|}^2-2|z_1\left|\right|z_2|$

$={\left(\right|z_1|-|z_2\left|\right)}^2$

$\Rightarrow |z_1-z_2|=\left|\right|z_1|-|z_2\left|\right|$