Explanation

(a)
$\left| \mathcal{z -}\frac{25}{\mathcal{z}} \right| \geq \left| \left| \mathcal{z} \right| - \frac{25}{\left| \mathcal{z} \right|} \right|\ \Rightarrow 24 \geq \ \left| \left| \mathcal{z} \right| - \frac{25}{\left| \mathcal{z} \right|} \right|$
$\Rightarrow \ - 24 \leq \left| \mathcal{\ z} \right| - \frac{25}{\left| \mathcal{z} \right|} \leq 24$
or $- 24\left| \mathcal{z} \right| \leq \left| \mathcal{z} \right|^{2} - 25 \leq 24|\mathcal{z|}$
$\therefore\ \ \left| \mathcal{z} \right|^{2} + 24\left| \mathcal{z} \right| - 25 \geq 0\ and\ \left| \mathcal{z} \right|^{2} - 24\left| \mathcal{z} \right| - 25 \leq 0$
$\Rightarrow \ \ \left( \left| \mathcal{z} \right| + 25 \right)\left( \left| \mathcal{z} \right| - 1 \right) \geq 0\ \ and\ (\left| \mathcal{z} \right| - 25)(\left| \mathcal{z} \right| + 1) \leq 0\ \$
$\therefore\ \ \left| \mathcal{\ z} \right| - 1 \geq 0\ and\ \left| \mathcal{z} \right| - 25 \leq 0$
Hence, $1 \leq |\mathcal{z}| \leq 25$
or $1 \leq |\mathcal{z -}0| \leq 25$