Home
Class 12
MATHS
(1 + omega) (1 + omega^(2)) (1 + omega^(...

` (1 + omega) (1 + omega^(2)) (1 + omega^(3)) (1 + omega^(4)) (1 + omega^(5)) (1 + omega^(6)) …. (1 + omega^(3n)) = `

A

`2^(3n)`

B

`2^(2n)`

C

`2^(n)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise EXERCISE -II|126 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise ADDITIONAL EXERCISE|17 Videos

  • CIRCLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|164 Videos

  • DEFINITE INTEGRALS

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

Similar Questions

Explore conceptually related problems

(1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega^(7)) (1 - omega^(8)) =

1 + omega + omega^(2) + ….. + omega^(300)

(1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+omega^(3n))

(1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + omega^(8)) to 2n factors =

(1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^(8))

(1- omega + omega^(2))^(7) + (1 + omega - omega^(2))^(7) =

If 1 , omega + omega^(2) are the cube roots of unity prove that (i) (1 - omega + omega^(2))^(6) + (1 - omega^(2) + omega)^(6) = 128 = ( 1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7) (ii) ( a+ b) ( aomega+b omega^(2))( a omega^(2) + b omega) = a^(3) + b^(3) (iii) x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

If 1 , omega , omega^(2) are the cube roots of unity prove that (1 - omega + omega^(2))^(6) + ( 1 - omega ^(2) + omega)^(6) = 128 = (1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7)

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….. to 2n factors

AAKASH SERIES-COMPLEX NUMBERS-EXERCISE - I
  1. The value of sqrt(15 + 8i) + sqrt(15 - 8i) is equal to

    Text Solution

    |

  2. If n is a multiple of 3 then omega^(n) + omega^(2n) =

    Text Solution

    |

  3. (1 + omega) (1 + omega^(2)) (1 + omega^(3)) (1 + omega^(4)) (1 + omega...

    Text Solution

    |

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

    Text Solution

    |

  5. The value of ((- 1 + sqrt-3)/(2))^(26) + ((- 1 - sqrt-3)/(2))^(26) is ...

    Text Solution

    |

  6. If (1 + omega)^(7) = A + B omega then (A , B) =

    Text Solution

    |

  7. If |3z-2|=5 then the locus of z is

    Text Solution

    |

  8. If |z -2 - 3i| = 5 then the locus of z = x +iy is

    Text Solution

    |

  9. The equation |z-1|^(2) + |z+1|^(2) = 2 represents

    Text Solution

    |

  10. If Re (z^2)=2 then the locus of z is

    Text Solution

    |

  11. If amp (z-i) =pi//3 then the locus of z is

    Text Solution

    |

  12. The locus of Z satisfying |z| + |z - 1| = 3 is

    Text Solution

    |

  13. If the amplitude of z - 2 - 3i " is " pi//4 , then the locus of z = x ...

    Text Solution

    |

  14. The complex number (1 + 2i)/(1 - i) lies in the

    Text Solution

    |

  15. If three complex number are in A.P then they lie on

    Text Solution

    |

  16. In the Argand plane, the points represented by the complex numbers 2-6...

    Text Solution

    |

  17. The condition for the points z(1) , z(2) , z(3) , z(4) taken in order ...

    Text Solution

    |

  18. The equation of the line joining the points represented by 2- 3i and -...

    Text Solution

    |

  19. The number of complex number z such |z-1|=|z+1|=|z-i| equals

    Text Solution

    |

  20. Statement - I : If z(1) and z(2) are two nonzero complex numbers such ...

    Text Solution

    |