I would start byfindingthe primitive roots then constructing the minimal polynomial from that.

The twelfth roots of unity, of course, satisfy the equation . They are of the form with n from 0 to 11: 1, , , , , , , , , , , and .

Aprimitiveroot is one that does NOT satisfy for any smaller value of n which removes 1, -1, i, and -i. What about cube roots?

It might help to note that is equivalent to

.