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Question: The maximum value of \|z\| satisfies the condition \(\left| z + \frac{2}{z} \right|\)= 2 is –...

The maximum value of |z| satisfies the condition ∣z+2z∣\left| z + \frac{2}{z} \right|= 2 is –

A

3–1\sqrt{3}–1

B

3+1\sqrt{3} + 1

C

3\sqrt{3}

D

2+3\sqrt{2} + \sqrt{3}

Answer

3+1\sqrt{3} + 1

Explanation

Solution

Sol. | z | = ∣z+2z–2z∣\left| z + \frac{2}{z}–\frac{2}{z} \right|£∣z+2z∣\left| z + \frac{2}{z} \right|+ 2∣z∣\frac{2}{|z|}

Ž | z | £ 2 + 2∣z∣\frac{2}{|z|}Ž (| z | – 1)2 £ 3

Ž1 – 3\sqrt{3}£| z | £ 1 + 3\sqrt{3}