The maximum distance from the origin of coodrinates to the point $z$ satisfying the equation $∣ ∣ ∣ z + \frac{1}{z} ∣ ∣ ∣ = a$ is

\frac{1}{2} (\sqrt{a^{2} + 1} + a)

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\frac{1}{2} (\sqrt{a^{2} + 2} + a)

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\frac{1}{2} (\sqrt{a^{2} + 4} + a)

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N o n e o f t h e s e

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Solution

The correct option is D $N o n e o f t h e s e$

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The maximum distance from the origin of coordinates to the point z satisfying the equation $∣ ∣ z + \frac{1}{z} ∣ ∣$ =a is

∣ ∣ ∣ z + \frac{1}{z} ∣ ∣ ∣ = a,

| z |

\frac{1}{2} [a + \sqrt{(a^{2} + 4)}]

\frac{1}{2} [a - \sqrt{(a^{2} + 4)}]

| z + \frac{1}{2} | = 1

z, (z \neq 0)

z

\frac{\sqrt{5} + 1}{2}

| z + \frac{1}{z} | = 1

\frac{1 + \sqrt{5}}{2}

The maximum value of |z| satisfying the equation $\frac{1}{12} (z + ¯ ¯ ¯ z)^{2} = 1 - \frac{1}{3} | z |^{2}$ is:

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