Home
Class 12
MATHS
If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1)...

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`

Promotional Banner

Topper's Solved these Questions

  • DE MOIVRE'S THEOREM

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Very Short Answer Questions|2 Videos

  • DE MOIVRE'S THEOREM

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Short Answer Questions|3 Videos

  • DE MOIVRE'S THEOREM

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Textual Exercise (EXERCISE - 2 (a) )|11 Videos

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise LAQ|1 Videos

  • DEFINITE INTEGRALS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Long Answer Question|3 Videos

Similar Questions

Explore conceptually related problems

If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, then the value of (3-alpha)(3-alpha^2)…...(3-alpha^(n-1)) is

If 1,alpha,alpha^2,…,alpha^(n-1) are the n^(th) roots of unity show that sum_(r=1)^(n-1)r(alpha_r+alpha_(n-r))=-n .

If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity then (1-alpha_1)(1-alpha_2)…..(1-alpha_(n-1))=

If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+4alpha^3+….+nalpha^(n-1)=-(n)/(1-alpha)

1,alpha_1,alpha_2,alpha_3…..alpha_(n-1) are the n^(th) roots of unity and n is an even natural number ,then (1+alpha_1)(1+alpha_2)(1+alpha_3)….(1+alpha_(n-1))=

If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity and n is an odd natural number then (1+alpha_1)(1+alpha_2)…..(1+alpha_(n-1))=

If 'alpha' be the non-real n^(th) roots of unity, then 1+3alpha+5alpha^2+…...(2n-1)alpha^(n-1) is equal to

If alpha_1 , alpha_2 ,……….,alpha_n are the roots of x^n + px + q = 0 , then (alpha_n - alpha_1) (alpha_n - alpha_2) ………(alpha_n - alpha_(n-1) ) =

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DE MOIVRE'S THEOREM-EXERCISE - 2 (b)
  1. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  2. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  3. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  4. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  5. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  6. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

  7. If 1 , omega , omega^(2) are the cube roots of unity , then find the ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Solve the following equations. x^(9) - x^(5) + x^(4) - 1 = 0

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If the cube roots of unity are 1 , omega , omega^(2), then find the r...

    Text Solution

    |

  14. Find the product of all the values of (1 + i)^(4//5).

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^...

    Text Solution

    |

  19. Show that one value of ((1 + sin . pi/8 + i cos . pi/8)/(1 + sin . p...

    Text Solution

    |

  20. Solve (x - 1)^n =x^n, where n is a positive integer.

    Text Solution

    |