Explanation

(c)
$\left| \mathcal{z -}2 \right| = \min{\{\left| \mathcal{z -}1 \right|,\ \left| \mathcal{z -}5 \right|\}}$
$ie,\ \left| \mathcal{z -}2 \right| = \left| \mathcal{z -}1 \right|,\ where\ \left| \mathcal{z -}1 \right| < |z - 5|$
$\Rightarrow \ \ Re\left( \mathcal{z} \right) = \frac{3}{2}$ which satisfy $\left| \mathcal{z -}1 \right| < |z - 5|$
Also, $\left| \mathcal{z -}2 \right| = \left| \mathcal{z -}5 \right|,$ where $\left| \mathcal{z -}5 \right| < |z - 1|$
$\Rightarrow \ \ Re\left( \mathcal{z} \right) = \frac{7}{2}$ which satisfy $\left| \mathcal{z -}5 \right| < \left| \mathcal{z -}1 \right|$