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If $\left|z+\frac{2}{z}\right|=2$, then the maximum value of $|z|$ is
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The correct answer is:
1 + √3
Given, $\left|z+\frac{2}{z}\right|=2$
$\begin{aligned} & \Rightarrow|z| \leq 2+\left|\frac{2}{z}\right| \Rightarrow|z|^2-2|z|-2 \leq 0 \\ & \Rightarrow|z| \in[0,(1+\sqrt{3})]\end{aligned}$
$|Z|_{\text {max }}=1+\sqrt{3}$
$\begin{aligned} & \Rightarrow|z| \leq 2+\left|\frac{2}{z}\right| \Rightarrow|z|^2-2|z|-2 \leq 0 \\ & \Rightarrow|z| \in[0,(1+\sqrt{3})]\end{aligned}$
$|Z|_{\text {max }}=1+\sqrt{3}$
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