Home
Class 12
MATHS
If w is a complex cube root of unity, th...

If `w` is a complex cube root of unity, then value of `=|a_1+b_1w a_1w^2+b_1c_1+b_1 w a_2+b_2w a_2w^2+b_2c_2+b_2 w a_3+b_3w a_3w^2+b_3c_3+b_3 w |` is a. 0 b. `-1` c. `2` d. none of these

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

if w is a complex cube root to unity then value of Delta =|{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)bar(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)bar(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)bar(w)):}| is

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

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

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

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 cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If omega is a complex nth root of unity, then underset(r=1)overset(n)(ar+b)omega^(r-1) is equal to

If omega is a cube root of unity and (omega-1)^7=A+Bomega then find the values of A and B

If 1, omega omega^(2) are the cube roots of unity show that (1 + omega^(2))^(3) - (1 + omega)^(3) = 0

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

CENGAGE-DETERMINANTS-All Questions
  1. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

    Text Solution

    |

  2. If the equation 2x+3y+1=0,3x+y-2=0,a n da x+2y-b=0 are consistent, ...

    Text Solution

    |

  3. If w is a complex cube root of unity, then value of =|a1+b1w a1w^2+b1c...

    Text Solution

    |

  4. Let f(x)=|cos(x+x^2)sin(x+x^2)- cos(x+x^2)...

    Text Solution

    |

  5. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

    Text Solution

    |

  6. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  7. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

    Text Solution

    |

  8. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

    Text Solution

    |

  9. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

    Text Solution

    |

  10. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

    Text Solution

    |

  11. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

    Text Solution

    |

  12. " if " x(i) =a(i) b(i) C(i) i= 1,2,3 are three- digit positive integer...

    Text Solution

    |

  13. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

    Text Solution

    |

  14. If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)...

    Text Solution

    |

  15. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n db x+3b y-c=0 ...

    Text Solution

    |

  16. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

    Text Solution

    |

  17. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

    Text Solution

    |

  18. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

    Text Solution

    |

  19. Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

    Text Solution

    |

  20. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+...

    Text Solution

    |