Algebra
# Roots of Unity

What is the complex solution set of the equation \(z^4-1=0\)?

Which of these is a solution to the equation \(z^6=12\)?

Let \(U_n\) denote the set of all \(n^\text{th}\) roots of unity.

If \(U_a=\{yz\mid y\in U_3,\ z\in U_5\}\), then \(a=\ ?\)

Which of these is a solution to the following equation?

\(x^5+x^4+x^3+x^2+x+1=0\)

*not necessarily* an \(n^\text{th}\) root of unity?

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