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Arithmetic Progression

If | z -2/ z ...

Question

If $∣ ∣ \begin{matrix} z - \frac{2}{z} \end{matrix} ∣ ∣ = 1$ then Range of $| Z |$ is

A

[0, 1]

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B

[1, 2]

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C

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D

[0, 2]

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Solution

The correct option is B
[1, 2]

$| | Z_{1} | - | Z_{2} | | \leq | Z_{1} \pm Z_{2} | ∣ ∣ r - \frac{2}{r} ∣ ∣ \leq 1, | z | = r - 1 \leq r - \frac{2}{r} \leq 1 - 1 \leq r \leq 2$

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