A) \[\sqrt{3}+1\]
B) \[\sqrt{5}+1\]
C) \[2\]
D) \[2+\sqrt{2}\]
Correct Answer: B
Solution :
Now, \[|z|\left| \left( z-\frac{4}{z} \right)+\frac{4}{z} \right|\] \[\Rightarrow \] \[|z|\le \left| z-\frac{4}{z} \right|+\left| \frac{4}{z} \right|\] \[\Rightarrow \] \[|z|\le 2+\frac{4}{|z|}\] \[\left( \because \left| z-\frac{4}{z} \right|=2 \right)\] \[\Rightarrow \] \[\Rightarrow |z{{|}^{2}}-2|z|-4\le 0\] \[\Rightarrow \] \[(|z|-(\sqrt{5+1}))(|z|-(1-\sqrt{5}))\le 0\] \[\Rightarrow \] \[1-\sqrt{5}\le |z|\le \sqrt{5}+1\]
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