Question

Consider the sixth roots of unity and choose ALL correct responses

A. The argument of any sixth root of unity is a multiple of 3
B. If z is a sixth root of unity, then z2 is also a sixth root of unity
C. If z is a sixth root of unity, then z is also a 12th root of unity
D. If z is a sixth root of unity, then z is a cube root of unity
E. If z is a sixth root of unity, then −z is also a sixth root of unity

Answer 1

Here are the six sixth root of unity:
\[
\large \left\{1,e^{\frac{i \pi
}{3}},e^{\frac{2 i \pi
}{3}},-1,e^{-\frac{2 i \pi
}{3}},e^{-\frac{i \pi
}{3}}\right\}
\]
They are the solutions of
\[
z^6 =1
\]

Answer 2

It easy to check which statement is true.