Question

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

• A. Re(z) > 0
• B. Re(z) < 0
• C. Re(z) > 2
• D. None of these

Answer 1

The correct option is D None of these

Given inequality $\mid z-4\mid <\mid z-2\mid$
$\Rightarrow \mid z-4{\mid }^2<\mid z-2{\mid }^2\Rightarrow (x-4{)}^2+y^2<(x-2{)}^2+y^2$
$\Rightarrow 4x>12\Rightarrow Re\left(z\right)>3$