Question

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

Answer 1

`abs(z) = (1+sqrt(5))/2`

Explanation:

See this question:

For `zinCC`, if `|z + 1/z| = a`, then What are the maximum and minimum values of `|z|`?

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`