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 of these

Answer 1

The correct option is A 25

The maximum value would be when
$|z-\frac{25}{z}|$
$=|z|-\frac{25}{|z|}=24$
$=|z{|}^2-25=24|z|$
$|z{|}^2-24|z|-25=0$
$|z{|}^2-25|z|+|z|-25=0$
$|z|(|z|-25)+1(|z|-25)=0$
$(|z|+1)(|z|-25)=0$
$|z|=-1$ not possible
And $|z|=25$