AP EAMCET · Maths · Complex Number
If \(\left|z-\frac{2}{z}\right|=2\), then the greatest value of \(|z|\) is
- A \(\sqrt{3}-1\)
- B \(\sqrt{3}\)
- C \(\sqrt{3}+1\)
- D \(\sqrt{3}+2\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3}+1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Given }\left|z-\frac{2}{z}\right|=2 \\ & \Rightarrow|| z\left|-\frac{2}{|z|}\right| \leq\left|z-\frac{2}{z}\right|=2 \\ & \Rightarrow|z|-\frac{2}{|z|} \leq 2 \Rightarrow|z|^2-2|z|-2 \leq 0 \\ & \Rightarrow|z| \leq \frac{1 \pm \sqrt{4+8}}{2} \leq…
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