Question

The complex number $z$ satisfies the condition $|z-\frac{25}{z}|=24$. The maximum distance from the origin of co-ordinates to the point $z$ is

• A. $25$
• B. $30$
• C. $32$
• D. None

Answer 1

The correct option is A $25$

$|z-\frac{25}{z}|\le |z|-\frac{25}{|z|}$

$24\le \frac{|z{|}^2-25}{|z|}$

$|z{|}^2-25|z|+|z|-25\ge 0$

$(|z|-25)(|z|+1)\ge 0$

$|z|-25=0$

$|z|=25$