WBJEE · Maths · Complex Number
The maximum value of \(|x|\), when the complex number \(z\) satisfies the condition \(\left|z+\frac{2}{z}\right|=2\) is
- A \(\sqrt{3}\)
- B \(\sqrt{3}+\sqrt{2}\)
- C \(\sqrt{3}+1\)
- D \(\sqrt{3}-1\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3}+1\)
Step-by-step Solution
Detailed explanation
We have the identity, \[ \begin{aligned}|z|=\left|z+\frac{2}{z}-\frac{2}{z}\right| \leq\left|z+\frac{2}{z}\right|+\left|\frac{2}{z}\right| \\ \Rightarrow \quad|z| \leq 2+\frac{2}{|z|} \end{aligned} \] \(\Rightarrow \quad|z|^{2} \leq 2|z|+2\)…
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