Home
Class 12
MATHS
If 1 , omega , omega^(2) are the cube ro...

If `1 , omega , omega^(2)` are the cube roots of unity, then prove that
`( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz`

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, omega, omega ^(2) are the cube roots of unity , then w^2=

If 1 , omega , omega^(2) are the cube roots of unity , then (x + y + z) (z + y omega + zomega^(2)) ( x + y omega^(2) + z omega) =

If 1 , omega , omega^(2) are the cube roots of unity prove that x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

If 1 , omega , omega^(2) are the cube roots of unity, then prove that (2 - omega)(2 -omega^(2)) (2 - omega^(10)) ( 2 - omega^(11)) = 49 .

If 1 , omega , omega^(2) are the cube roots of unity, then prove that 1/(2 + omega) + 1/(1+2 omega) = 1/(1 + omega) .

If 1, omega , omega^(2) are the cube roots of unity, then prove that 1/(2 + omega) + 1/(1 + 2 omega) = 1/( 1 + omega) .

If 1 , omega , omega^(2) are the cube roots of unity , then the roots of (x - 1)^(3) + 8 = 0 are

If 1 , omega , omega^(2) are the cube roots of unity , then the roots of (x - 2)^(2) + 1 = 0 are

If 1 , omega , omega^(2) are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3) + (a omega + b omega^(2))^(3) + ( a omega^(2) + b omega)^(3) =

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Prove that - omega, " and " - omega^(2) are the roots of z^(2) - z...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |