Solve the equation `z^(3) = barz (z ne 0)`

Explanation

As `zne0,`
`|z^(3)|=|bar(z)|`
`implies" "|z|^(3)=|bar(z)|`
`implies" "|z|^(3)=|z|`
`implies" "|z|=1`
`:." "z^(3)=bar(z)`
`implies" "z^(4)=zbar(z)=|z|^(2)=1`
`implies" "z=+-1,+-i`