Home
Class 12
MATHS
Let omega be the complex number cos(2pi/...

Let `omega` be the complex number `cos(2pi/3)+isin(2pi/3)` Then the number of distinct complex numbers z satisfying `abs[[z+1,omega,omega^2],[omega,(z+omega^2),1],[omega^2,1 ,z+omega]]=0` is equals to

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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

If omega be an imaginary cube root of 1 then the value of |[1,omega^2,omega],[omega,1,omega^2],[omega^2,omega,1]| is

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If 1, omega, omega^(2) are the cube roots of unity, then the value of |(1,omega^(n),omega^(2n)),(omega^(n),omega^(2n),1),(omega^(2n),1,omega^(n))| is equal to -

(b) answer any one of the foll.: (i) prove without expanding |[1,omega,omega ^2],[omega ,omega ^2 ,1],[omega ^2,1, omega]|=0 wher w is an imaginary cube root of unity.

Find the complex number satisfying system of equation z^(3)=-((omega))^(7) and z^(5).omega^(11)=1

Evaluate abs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) were omega is an imaginary cube root of unity.

If omega is the complex cube root of unity, then find omega+1/omega +1/omega^2

If omega is the complex cube root of unity, then find (1+omega-omega^2)^3

If omega is the complex cube root of unity, then find (1-3omega+omega^2)^3

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

    Text Solution

    |

  2. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

    Text Solution

    |

  3. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

    Text Solution

    |

  4. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

    Text Solution

    |

  5. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

    Text Solution

    |

  6. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

    Text Solution

    |

  7. If A , B ,a n dC are the angles of triangle, show that the system of...

    Text Solution

    |

  8. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

    Text Solution

    |

  9. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

    Text Solution

    |

  10. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

    Text Solution

    |

  11. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

    Text Solution

    |

  12. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  13. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

    Text Solution

    |

  14. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  15. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  16. "If " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fol...

    Text Solution

    |

  17. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

    Text Solution

    |

  18. Factorize: a x+b x+a y+b y +a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+...

    Text Solution

    |

  19. If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...

    Text Solution

    |

  20. The sum of values of p for which the equations x+y+z=1, x+2y +4z...

    Text Solution

    |