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Q.
If the complex number $z$ satisfies the condition $|z| \geq 3$, then find the least value of $|z+(1 / z)|$.
Complex Numbers and Quadratic Equations
Solution:
$\left|z+\frac{1}{z}\right| \geq|| z\left|-\frac{1}{|z|}\right|$
The least value of occurs when $| z |=3$
$\left| z +\frac{1}{ z }\right|_{\min }=3-\frac{1}{3}=\frac{8}{3}$