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

MCQ

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

A
$\operatorname{Re}(z)>0$
B
$\operatorname{Re}(z)<0$
C
$\operatorname{Re}(z)>2$
✓
$\operatorname{Re}(z)>3$

✓

Answer

Correct option: D.

$\operatorname{Re}(z)>3$

(D)
$|z-4|<|z-2|$
$\Rightarrow|z-4|^2<|z-2|^2$
$\Rightarrow(x-4)^2+y^2<(x-2)^2+y^2$
$\Rightarrow 4 x>12$
$\Rightarrow \operatorname{Re}( z )>3$

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