Home
Class 12
MATHS
Prove that - omega, " and " - omega^(2...

Prove that ` - omega, " and " - omega^(2)` are the roots of ` z6(2) - z + 1 = 0`, where `omega " and " omega^(2)` are the complex cube roots of unity .

Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE - 6 (LONG ANSWER QUESTIONS)|21 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise ADDITIONAL EXERCISE|7 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE - 6 (VERY SHORT ANSWER QUESTIONS)|17 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

Prove that - omega, " and " - omega^(2) are the roots of z^(2) - z + 1 = 0 , where omega " and " omega^(2) are the complex cube roots of unity .

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 prove that x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

If |z|=3 , then area of the triangle whose sides are z , omegaz and z +omegaz (where omega is a complex cube root of unity) is

If |z| =3 , the area of the triangle whose sides are z , omega z and z + omega z (where omega is a complex cube root of unity) is

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 and omega^(2) are the cube roots of unity, then (a+b+c) (a+b omega+c omega^(2))(a+b omega^(2) +c omega)=

If x=p+q,y=pomega+q omega^(2) and z=p omega^(2)+q omega , where omega is a complex cube root of unity, then xyz equals to

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

AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE - 6 (SHORT ANSWER QUESTIONS)
  1. Find all the values of following . (-16)^(1//4)

    Text Solution

    |

  2. Find all the values of following . (-32)^(1//5)

    Text Solution

    |

  3. Find all the values of the following (sqrt3+i)^(1//4)

    Text Solution

    |

  4. Find all the values of following . (1 - I sqrt3)^(1//3)

    Text Solution

    |

  5. Find all the values of following . (1 + i)^(2//3)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that - omega, " and " - omega^(2) are the roots of z6(2) - z...

    Text Solution

    |

  18. If alpha, beta are the roots of the equation x^(2) + x + 1 = 0 then ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |