Question

The complex number $z$ satisfies the condition $\left|z-\frac{25}{z}\right|=24$. Then the maximum distance from the origin to the point '$z$' in the argand plane is

• A. 20
• B. 25
• C. 30
• D. 35

Answer 1

Answer: (B)

25

$|z|=|z-\frac{25}{z}+\frac{25}{z}|\le 24+\frac{25}{|z|}$
$\therefore$ $|z{|}^2-24|z|-25\le 0.$
$\therefore$ $(|z|-25)(|z|+1)\le 0.,\Rightarrow |z|\le 25.$
Hence maximum distance of z from origin is 25.