A) \[\sqrt{3}-1\]
B) \[\sqrt{3}+1\]
C) \[\sqrt{3}\]
D) \[\sqrt{2}+\sqrt{3}\]
Correct Answer: B
Solution :
\[\left| z+\frac{2}{z} \right|=2\Rightarrow |z|-\frac{2}{|z|}\le 2\]Þ\[|z{{|}^{2}}-2|z|-2\le 0\] \[|z|\le \frac{2\pm \sqrt{4+8}}{2}\le 1\pm \sqrt{3}\]. Hence max. value of \[|z|\]is \[1+\sqrt{3}\]
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