Question

If the complex number $z$ satisfies the condition $|z|\ge 3$, then find the least value of $|z+(1/z)|$.

Answer 1

Answer: 2.67

$\left|z+\frac{1}{z}\right|\ge ||z\left|-\frac{1}{|z|}\right|$
The least value of occurs when $|z|=3$
${\left|z+\frac{1}{z}\right|}_{\min }=3-\frac{1}{3}=\frac{8}{3}$