Home
Class 12
MATHS
If omega is a complex cube root of unity...

If `omega` is a complex cube root of unity, then `(a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=`

A

`1`

B

`omega`

C

`omega^(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos

  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos

  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

If omega pm 1 is a cube root of unity, show that (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1

If omega ne 1 is a cube root of unity, then show that (a+bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+aomega+bomega^(2))=1

If omega pm 1 is a cube root of unity, show that (1 - omega + omega^(2))^(6) + (1 + omega - omega^(2))^(6) = 128

If omega is a cube root of unity, then the value of (1 - omega + omega^2)^4 + (1 + omega - omega^2)^(4) is ……….

If 1, omega omega^(2) are the cube roots of unity then show that (1 + 5omega^(2) + omega^(4)) ( 1 + 5omega + omega^(2)) ( 5 + omega + omega^(5)) = 64.

If omega is the cube root of unity, then then value of (1 - omega) (1 - omega^(2))(1 - omega^(4))(1 - omega^(8)) is

If omega is a complex cube root of unity, then the value of sin{(omega^(10)+omega^(23))pi- (pi)/(6)} is

If omega pm 1 is a cube root of unity, show that (1 + omega) (1 + omega^(2))(1 + omega^(4))(1 + omega^(8))…(1 + omega^(2^(11))) = 1

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. The least integer k which makes the roots of the equation x^(2)+5x+k=0...

    Text Solution

    |

  2. If x^(2)px+q=0 is the quadratic equation whose roots are a-2" and "b-2...

    Text Solution

    |

  3. If omega is a complex cube root of unity, then (a+b omega+c omega^(2))...

    Text Solution

    |

  4. If alpha" and "beta are complex cube roots of unity and x=a alpha+ b b...

    Text Solution

    |

  5. If a,b and c are distinct positive real numbers in A.P, then the roots...

    Text Solution

    |

  6. If z(1),z(2)" and "z(3) are any three complex numbers, then the fourth...

    Text Solution

    |

  7. Let a,b be the solutions of x^(2)+px+1=0 and c, d be the solutions of ...

    Text Solution

    |

  8. If alpha" and "beta are the solutions of the quadratic equation ax^(2)...

    Text Solution

    |

  9. A point P which represents a complex number Z moves such that |Z-Z(1)|...

    Text Solution

    |

  10. ((cos theta+isin theta)^4)/((sin theta+icos theta)^5)=?

    Text Solution

    |

  11. The quadratic equation whose roots are twice the roots of 2x^(2)-5x+2=...

    Text Solution

    |

  12. If alpha+beta=4" and "alpha^(3)+beta^(3)=44" the "alpha, beta are the ...

    Text Solution

    |

  13. The coefficient of x in x^(2)+px+q=0 was taken as 17 in place of 13 an...

    Text Solution

    |

  14. The value of (cos"" (pi)/(2)+isin ""(pi)/(2))(cos ((pi)/(2^2))+isin((p...

    Text Solution

    |

  15. (2-omega)(2-omega^(2))(2-omega^(10))(2-omega^(11))="……..", where omega...

    Text Solution

    |

  16. If Zr =cos ((pi)/(2^r))+isin((pi)/(2^r)) then Z(1).Z(2).Z(3)"…….." upt...

    Text Solution

    |

  17. In the Argand diagram OAP is an isosceles right angled triangle, right...

    Text Solution

    |

  18. The real part of [1+cos(pi/5)+isin (pi/5)]^(-1)

    Text Solution

    |

  19. For a ne b, if the equation x^(2)+ax+b=0" and "x^(2)+bx+a=0 have a com...

    Text Solution

    |

  20. If (2z1)/(3z2) is purely imaginary then |(z(1)-z(2))/(z(1)+z(2))|

    Text Solution

    |