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

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

A

3\sqrt{3}– 1

B

3\sqrt{3}+1

C

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

D

3\sqrt{3}

Answer

3\sqrt{3}+1

Explanation

Solution

Sol. If ∣z±az∣\left| z \pm \frac{a}{z} \right| = b

| z |max = b2+4a+b2\frac{\sqrt{b^{2} + 4a} + b}{2}