JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z \neq 0\) be a complex number such that \(\left| z -\frac{1}{ z }\right|=2\), then the maximum value of \(|z|\) is.
- A \(\sqrt{2}\)
- B \(1\)
- C \(\sqrt{2}-1\)
- D \(\sqrt{2}+1\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}+1\)
Step-by-step Solution
Detailed explanation
\(| z -1 / z |=2\) || \(z \left|-\frac{1}{| z |}\right| \leq\left| z -\frac{1}{ z }\right| \leq| z |+\frac{1}{| z |}\) \(\left| r -\frac{1}{ r }\right| \leq 2 \leq r +\frac{1}{ r }\) \(\left| r -\frac{1}{ r }\right| \leq 2 \& r +\frac{1}{ r } \geq 2\) always true…
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