ok lets check this
1=1
1=cuberoot(1)
1=cuberoot(-1*-1*1)
1=cuberoot(-1)*cuberoot(-1)*cuberoot(1)
1=cuberoot(iota)*cuberoot(iota)*cuberoot(1)

cubing both sides

1=iota*iota*1
1=-1*1
1=-1