AIEEE 2009 (Offline)Question 1
If $\left|z-\frac4z\right|=2$, then the maximum value of $|z|$ is equal to :
Complex Numbers
Solution
$|z|-\frac4{|z|}\le\left|z-\frac4z\right|=2$, so $r^2-2r-4\le0$, $r\le1+\sqrt5$ (attained for $z$ purely imaginary). Maximum $|z|=\sqrt5+1$.