If z is a complex number with |z| geq 5,then | vedclass

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(C) We are given $|z| \geq 5$. Using the triangle inequality,we know that $|z + w| \geq ||z| - |w||$. Therefore,$\left|z + \frac{2}{z}\right| \geq ||z

Vedclass · Accepted Answer

$\frac{23}{5}$

Vedclass · Answer

(C) We are given $|z| \geq 5$. Using the triangle inequality,we know that $|z + w| \geq ||z| - |w||$. Therefore,$\left|z + \frac{2}{z}\right| \geq ||z| - \left|\frac{2}{z}\right|| = ||z| - \frac{2}{|z|}||$. Let $f(t) = t - \frac{2}{t}$ where $t = |z| \geq 5$. Since $f(t)$ is an increasing function for $t > 0$,the minimum value occurs at the smallest value of $t$,which is $t = 5$. Thus,$\left|z + \frac{2}{z}\right| \geq 5 - \frac{2}{5} = \frac{25-2}{5} = \frac{23}{5}$. The least value is $\frac{23}{5}$.

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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