Additional Concepts
-$$x ^ { 7 } - 1 = 0$$
A) $1 , \cos \left( 51.4 ^ { \circ } \right) + i \sin \left( 51.4 ^ { \circ } \right) , \cos \left( 102.9 ^ { \circ } \right) + i \sin \left( 102.9 ^ { \circ } \right) , \cos \left( 154.3 ^ { \circ } \right) + i \sin \left( 154.3 ^ { \circ } \right) , \cos \left( 205.7 ^ { \circ } \right) + i$ $\sin \left( 205.7 ^ { \circ } \right) , \cos \left( 257.1 ^ { \circ } \right) + i \sin \left( 257.1 ^ { \circ } \right) , \cos \left( 308.6 ^ { \circ } \right) + i \sin \left( 308.6 ^ { \circ } \right)$
B) $1 , \cos \left( 25.7 ^ { \circ } \right) + i \sin \left( 25.7 ^ { \circ } \right) , \cos \left( 51.4 ^ { \circ } \right) + i \sin \left( 51.4 ^ { \circ } \right) , \cos \left( 77.1 ^ { \circ } \right) + i \sin \left( 77.1 ^ { \circ } \right) , \cos \left( 102.9 ^ { \circ } \right) + i \sin \left( 102.9 ^ { \circ } \right)$, $\cos \left( 128.6 ^ { \circ } \right) + i \sin \left( 128.6 ^ { \circ } \right) , \cos \left( 154.3 ^ { \circ } \right) + i \sin \left( 154.3 ^ { \circ } \right)$
C) $1 , \cos \left( 51.4 ^ { \circ } \right) + i \sin \left( 51.4 ^ { \circ } \right) , \cos \left( 102.9 ^ { \circ } \right) + i \sin \left( 102.9 ^ { \circ } \right) , \cos \left( 154.3 ^ { \circ } \right) + i \sin \left( 154.3 ^ { \circ } \right) , \cos \left( 205.7 ^ { \circ } \right) + i$ $\sin \left( 205.7 ^ { \circ } \right) , \cos \left( 257.1 ^ { \circ } \right) + i \sin \left( 257.1 ^ { \circ } \right) , \cos \left( 308.6 ^ { \circ } \right) + i \sin \left( 308.6 ^ { \circ } \right) , - 1$
D) $- 1 , \cos \left( 25.7 ^ { \circ } \right) + i \sin \left( 25.7 ^ { \circ } \right) , \cos \left( 51.4 ^ { \circ } \right) + i \sin \left( 51.4 ^ { \circ } \right) , \cos \left( 77.1 ^ { \circ } \right) + i \sin \left( 77.1 ^ { \circ } \right) , \cos \left( 102.9 ^ { \circ } \right) + i \sin \left( 102.9 ^ { \circ } \right)$, $\cos \left( 128.6 ^ { \circ } \right) + i \sin \left( 128.6 ^ { \circ } \right) , \cos \left( 154.3 ^ { \circ } \right) + i \sin \left( 154.3 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The equation $x^7 - 1 = 0$ has roots that are the 7th roots of unity, which are $e^{2\pi i k/7}$ for $k = 0, 1, 2, \ldots, 6$. These correspond to angles $0^\circ, 51.4^\circ, 102.9^\circ, 154.3^\circ, 205.7^\circ, 257.1^\circ, 308.6^\circ$. Option A lists these angles correctly.

Additional Concepts - x7−1=0x ^ { 7 } - 1 = 0x7−1=0

Additional Concepts
- $x ^ { 7 } - 1 = 0$