Question

Show that the solutions for `1 + z^4 + z^3 + 2 z^2 =0` obey the condition `absz = 1` ?

Answer 1

`|z| = 1`

Explanation:

`"This is a symmetric equation. Those can be solved with the"`
`"substitution t = z + 1/z : "`
`=> t^2 + t = 0.`
`=> t = 0 or t = -1`
`=> z^2 + 1 = 0 or z^2 + z + 1 = 0`
`=> z = pm i or z = (-1 pm sqrt(3) i)/2`
`=> |z| = 1`

Answer 2

`absz = 1`

Explanation:

`1 + z^4 + z^3 + 2 z^2 = (1+z^2)(1+z+z^2) = 0`

then `absz = 1`