Read: Review Section 3.1.2 and read Section 3.1.3.
- Make sure to get the updated version of our book; Problem 3.27 was changed slightly.
Turn in: 3.21, 3.22, 3.23, 3.24, 3.27
- Take care in proving 3.24; you are really proving a bi-conditional: $z$ is an $n$th root of unity iff $z\in \{1,\zeta_n, (\zeta_n)^2,\ldots, (\zeta_n)^{n-1}\}$. But, one direction was proven in a previous problem.
- You can use Theorem 3.26 when you work on 3.27 even though you are not being asked to prove 3.26. To do this, you just need to determine one root of the given polynomial (by “solving for $x$”), and then you can apply 3.26.
- Remember that there are some hints in the back of the book, but please don’t look at them without trying yourself and with classmates first.
Please try (but do not turn in): 3.25, 3.26, 3.28
