Question:

Step 1: Let $r = |z|$. Apply the triangle inequality to $\left|z - \dfrac{25}{z}\right| = 24$: $$\left||z| - \left|\frac{25}{z}\right|\right| \leq \left|z - \frac{25}{z}\right| \leq |z| + \left|\frac{25}{z}\right|$$ $$\left|r - \frac{25}{r}\right| \leq 24 \leq r + \frac{25}{r}$$ Step 2: From $\left|r - \dfrac{25}{r}\right| \leq 24$, we get $-24 \leq r - \dfrac{25}{r} \leq 24$. Step 3: From $r - \dfrac{25}{r} \leq 24$: $r^2 - 24r - 25 \leq 0 \Rightarrow (r-25)(r+1) \leq 0 \Rightarrow r \leq 25$ (since $r > 0$). Step 4: From $r - \dfrac{25}{r} \geq -24$: $r^2 + 24r - 25 \geq 0 \Rightarrow (r+25)(r-1) \geq 0 \Rightarrow r \geq 1$ (since $r > 0$). Step 5: Therefore $1 \leq r \leq 25$, meaning the minimum distance from origin is $1$ and maximum distance is $25$. Step 6: The correct options are **(b) Maximum distance is 25** and **(c) Minimum distance is 1**.