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

May 21, 2016

$\left\mid z \right\mid = \frac{1 + \sqrt{5}}{2}$

Explanation:

See this question:

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

$\frac{a + \sqrt{{a}^{2} + 4}}{2} = \frac{1 + \sqrt{1 + 4}}{2} = \frac{1 + \sqrt{5}}{2}$

$\left\mid z + \frac{1}{z} \right\mid$ attains its maximum value for $z = \pm \frac{1 + \sqrt{5}}{2} i$