If $∣ ∣ ∣ z + \frac{1}{z} ∣ ∣ ∣ = 1$ $abs(z+1/z) = 1$ , then what is the maximum possible value of $| z |$ $abs(z)$ ?

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Answer 1 · 2016-05-21T13:53:28

$| z | = \frac{1 + \sqrt{5}}{2}$ $abs(z) = (1+sqrt(5))/2$

See this question:

In our current question $a=1$ and we are only interested in the maximum value:

$(a+sqrt(a^2+4))/2 = (1+sqrt(1+4))/2 = (1+sqrt(5))/2$

$abs(z+1/z)$ attains its maximum value for $z = +-(1+sqrt(5))/2 i$

If abs(z+1/z) = 1∣∣∣z+1z∣∣∣=1abs(z+1/z) = 1, then what is the maximum possible value of abs(z)|z|abs(z) ?