Question

If ${\alpha }_1,{\alpha }_2,...,{\alpha }_8$ are the $8$, $8th$ roots of unity, then

• A. ${\alpha }_1^3+{\alpha }_2^3+...+{\alpha }_8^3=24$
• B. ${\alpha }_1+{\alpha }_2+...+{\alpha }_8=1$
• C. ${\alpha }_1^{50}+{\alpha }_2^{50}+...+{\alpha }_8^{50}=0$
• D. ${\alpha }_1^{48}+{\alpha }_2^{48}+...+{\alpha }_8^{48}=0$

Answer 1

Answer: (C)

Correct answer is (c) ${\alpha }_1^{50}+{\alpha }_2^{50}+...+{\alpha }_8^{50}=0$