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If `1,alpha,alpha^2,alpha^3,…,alpha^(n-1)` be the `n^(th)` roots of unity, then prove that `1^p+alpha^p+(alpha^2)^p+(alpha^3)^p+…+(alpha^(n-1))^p={{:(0,if" "pnekn),(n,if" "p=kn):}" where p,k"epsilonN`

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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE - 6 (LONG ANSWER QUESTIONS)
  1. If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^...

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  2. If n is an integer then show that (1 + cos theta + i sin theta)^(n...

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  3. If alpha, beta are the roots of the equation x^(2) - 2x + 4 = 0 the...

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  4. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

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  5. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

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  6. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

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  7. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

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  8. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

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  9. If cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin g...

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  10. Solve the following equations. x^(4) - 1 = 0

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  11. Solve the following equations. x^(5) + 1 = 0

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  12. Solve the following equations. x^(4) + 1 = 0

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  13. Solve the following equations x^(11)-x^7+x^4-1=0

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  14. If ( 1 + x ) ^(n) = a(0) + a (1) x + a(2) x^(2) + ………. + a(n)x^(n...

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  15. If ( 1 + x ) ^(n) = a(0) + a (1) x + a(2) x^(2) + ………. + a(n)x^(n...

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  16. The common roots of the equation x^(12)-1=0,x^4+x^2+1=0 are

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  17. Find the number of 15^(th)roots of unity, which are also 25^(th) roots...

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  18. If z^(2) + z + 1 = 0, where z is a complex number , prove that ( z...

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  19. If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity,...

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  20. Prove the sum of 99t^(th) powers of the roots of the equation x^7-1 = ...

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