Home
Class 11
MATHS
If a^3+b^3+6a b c=8c^3&omega is a c...

If `a^3+b^3+6a b c=8c^3&omega` is a cube root of unity then: `a , b , c` are in `AdotPdot` (b) `a , b , c ,` are in `HdotPdot` `a+bomega-2comega^2=0` `a+bomega^2-2comega=0`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RESONANCE DPP|Exercise All Questions|3 Videos

  • CONIC SECTIONS

    RESONANCE DPP|Exercise All Questions|25 Videos

Similar Questions

Explore conceptually related problems

If omega is a cube root of unity then |(a,b,c),(b,c,a),(c,a,b)| has a factor

If omega pm 1 is a cube root of unity, the value of (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = ?

Let omega be a complex cube root of unity with 0

If omega is a cube root of unity, then find the value of the following: (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^2)/(c+comega+aomega^2)

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

RESONANCE DPP-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z1,z2,z3 are three distinct non-zero complex numbers and a ,b ,c in...

    Text Solution

    |

  2. Statement-1 : Let z be a complex number satisfying |z-3|lt=|z-1|,|z-3|...

    Text Solution

    |

  3. If a^3+b^3+6a b c=8c^3&omega is a cube root of unity then: a , b...

    Text Solution

    |

  4. The image of a complex number z in the imaginary axis is (A) z (...

    Text Solution

    |

  5. If z1,z2,z3 are the vertices of the A B C on the complex plane and ar...

    Text Solution

    |

  6. If 2x=-1+sqrt(3)i , then the value of (1-x^2+x)^6-(1-x+x^2)^6 is 32 (b...

    Text Solution

    |

  7. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

    Text Solution

    |

  8. Number of roots which are common to the equations x^3+2x^2+2x+1=0 and ...

    Text Solution

    |

  9. If z1,z2,z3,z4 be the vertices of a parallelogram taken in anticlockwi...

    Text Solution

    |

  10. Area bounded by a r g(z)=pi/3,A rg(z)=(2pi)/3 and A rg(z-2-i2sqrt(3))...

    Text Solution

    |

  11. The greatest value of the modulus of the complex number ' z ' satisfyi...

    Text Solution

    |

  12. The set of points on a Argand diagram which satisfy bot |z|lt=4&A ...

    Text Solution

    |

  13. The number of solutions of z^3+ z =0 is 2 (b) 3 (c) 4 (d) 5

    Text Solution

    |

  14. If omega is an imaginary cube root of unity, then the value of (p+q)^...

    Text Solution

    |

  15. If z0,z1 represent points P ,Q on the locus |z-1|=1 and the line se...

    Text Solution

    |

  16. Let z1=a+i b and z2=c+i d are two complex number such that |z1|=|z2|...

    Text Solution

    |

  17. The centre of a square is at the point with complex number z0=1+i and...

    Text Solution

    |

  18. Intercept made by the circle zbar z + alphabarz+baralpha z +r=0 on ...

    Text Solution

    |

  19. The triangle formed by complex numbers z ,i z ,i^2z is (a)Equilatera...

    Text Solution

    |

  20. If omega!=1 is n^(t h) root of unity, then value of sum(k=0)^(n-1)...

    Text Solution

    |