Solve the equation `z^6=-i`

Explanation

`z^6=-i=cos(3pi)/2+isin(3pi)/2`
`=cos((3pi)/2+2kpi)+isin((3pi)/2+2kpi)`
`cos(pi(4k+3))/2+isin(pi(4k+3))/2`
`z=[(cos(4k+3)pi)/2=isin((4k+3)pi)/2]^(1/6)`
`cos((4k+3)pi)/(12)=isin((4k+3)pi)/(12)`
`"where "k=0,2,3,4,5`