WBJEE · Maths · Complex Number
Find the maximum value of \(|z|\) when \(\left|z-\frac{3}{z}\right|=2,\) where \(z\) being a complex number.
- A \(1+\sqrt{3}\)
- B 3
- C \(1+\sqrt{2}\)
- D 1
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
We have, \(|z|=\left|z-\frac{3}{z}+\frac{3}{z}\right|\) \(\Rightarrow \quad|z| \leq\left|z-\frac{3}{z}\right|+\left|\frac{3}{z}\right|\) [using triangle inequality] \(\Rightarrow \quad|z| \leq 2+\left|\frac{3}{z}\right|\) \(\left[\because\left|z-\frac{3}{z}\right|=2\right]\)…
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