Question

The inequality $|z-4|<|z-2|$ represents the region given by,

• A. $\text{Re}(z)>0$
• B. $\text{Re}(z)<0$
• C. $\text{Re}(z)>3$
• D. None of these

Answer 1

Answer: (C)

Given $|z-4{|}^2<|z-2{|}^2$
$\Rightarrow |(x-4)+iy{|}^2<|(x-2)+iy{|}^2$
$\Rightarrow (x-4{)}^2+y^2<(x-2{)}^2+y^2$
$\Rightarrow -4x<-12$
$\Rightarrow 4x>12;x>3$
$\Rightarrow \text{Re}(z)>3$