Additional Concepts
-$$x ^ { 5 } - 1 = 0$$
A) $1 , \cos \left( 72 ^ { \circ } \right) + i \sin \left( 72 ^ { \circ } \right) , \cos \left( 144 ^ { \circ } \right) + i \sin \left( 144 ^ { \circ } \right) , \cos \left( 216 ^ { \circ } \right) + i \sin \left( 216 ^ { \circ } \right) , \cos \left( 288 ^ { \circ } \right) + i \sin \left( 288 ^ { \circ } \right)$
B) $- 1 , \cos \left( 72 ^ { \circ } \right) + i \sin \left( 72 ^ { \circ } \right) , \cos \left( 144 ^ { \circ } \right) + i \sin \left( 144 ^ { \circ } \right) , \cos \left( 216 ^ { \circ } \right) + i \sin \left( 216 ^ { \circ } \right) , \cos \left( 288 ^ { \circ } \right) + i \sin \left( 288 ^ { \circ } \right)$
C) $1 , \cos \left( 72 ^ { \circ } \right) + i \sin \left( 72 ^ { \circ } \right) , \cos \left( 144 ^ { \circ } \right) + i \sin \left( 144 ^ { \circ } \right) , \cos \left( 216 ^ { \circ } \right) + i \sin \left( 216 ^ { \circ } \right) , - 1$
D) $1 , \cos \left( 36 ^ { \circ } \right) + i \sin \left( 36 ^ { \circ } \right) , \cos \left( 108 ^ { \circ } \right) + i \sin \left( 108 ^ { \circ } \right) , \cos \left( 180 ^ { \circ } \right) + i \sin \left( 180 ^ { \circ } \right) , \cos \left( 252 ^ { \circ } \right) + i \sin \left( 252 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The equation $x^5 - 1 = 0$ can be solved using the formula for roots of unity, which gives solutions in the form of $e^{2\pi i k/n}$ for $k=0,1,...,n-1$ where $n=5$ in this case. This corresponds to $1, \cos(72^\circ) + i\sin(72^\circ), \cos(144^\circ) + i\sin(144^\circ), \cos(216^\circ) + i\sin(216^\circ), \cos(288^\circ) + i\sin(288^\circ)$, matching choice A.

Additional Concepts - x5−1=0x ^ { 5 } - 1 = 0x5−1=0

Additional Concepts
- $x ^ { 5 } - 1 = 0$