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

(A) $\operatorname{Re}(z)>0$

(B) $\operatorname{Re}(z)<0$

(C) $\operatorname{Re}(z)>2$

(D) None of these

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Best answer

SOLUTION —

$|(x-4)+i y|^2<|(x-2)+i y|^2 $

$\Rightarrow \quad(x-4)^2+y^2<(x-2)^2+y^2$

$\Rightarrow \quad 4 x>12 \Rightarrow\operatorname{Re}(z)>3$

So, The correct option will be (D).

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