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Question: If \(\left| z - \frac{1}{z} \right| = 1\), then:...

If ∣z−1z∣=1\left| z - \frac{1}{z} \right| = 1, then:

A

|z|max =1+52\frac{1 + \sqrt{5}}{2}

B

|z|min = 1+52\frac{1 + \sqrt{5}}{2}

C

|z|max = −1+52\frac{- 1 + \sqrt{5}}{2}

D

None of these

Answer

|z|max =1+52\frac{1 + \sqrt{5}}{2}

Explanation

Solution

Sol. ∣z±az∣=b\left| z \pm \frac{a}{z} \right| = b then |z|max. = b2+4a+b2\frac{\sqrt{b^{2} + 4a + b}}{2}

z|min. = b2+4a−b2\frac{\sqrt{b^{2} + 4a - b}}{2}