If $z$ is a complex number with $|z| \geq 5$. Then the least value of $\left|z+\frac{2}{z}\right|$ is

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Aicharya · Accepted Answer

We have given, $|z| \geq 5$ $ \begin{aligned} & 	ext { Now, }\left|z+\frac{2}{z}ight| \geq|z|-\left|\frac{2}{z}ight|=|| z\left|+\frac{2}{z}ight| \ & =|| z\left|+2\left(\frac{-1}{|z|}ight)ight| \geq\left|5-\frac{2}{5}ight| \ & 	herefore\left|z+\frac{2}{z}ight| \geq \frac{23}{5} \end{aligned} $ Thus, the least value of $|\quad \underline{2}|$ is $\frac{23}{}$

If $z$ is a complex number with $|z| \geq 5$. Then the least value of $\left|z+\frac{2}{z}\right|$ is

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