Home
Class 11
MATHS
a ,b , c are integers, not all simultane...

`a ,b , c` are integers, not all simultaneously equal, and `omega` is cube root of unity `(omega!=1)` , then minimum value of `|a+bomega+comega^2|` is `0` b. `1` c. `(sqrt(3))/2` d. `1/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are distinct odd integers and omega is non real cube root of unity, then minimum value of | a omega^2 + b+ comega| , is

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

If a,b,c are distinct integers and omega(ne 1) is a cube root of unity, then the minimum value of |a+bomega+comega^(2)|+|a+bomega^(2)+comega| is

If omega is a cube root of unity, then 1+ omega^(2)= …..

If 1, omega,omega^(2) are cube roots of unity then the value of (2+2omega-3omega^(2))^(3) is

If 1 , omega, omega^(2) are cube roots of unity then the value of (5+2omega +5omega^(2))^(3) is

If 1 , omega, omega^(2) are cube roots of unity then the value of (3 + 5omega+3omega^(2))^(3) 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 cube root of unity but not equal to 1, then minimum value of abs(a+bomega+comega^(2)) , (where a,b and c are integers but not all equal ), is

If omega is the complex cube root of unity, then the value of omega+omega ^(1/2+3/8+9/32+27/128+………..) ,

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=...

    Text Solution

    |

  2. The value of i^(1+3+5+.....+(2n+1)) is.

    Text Solution

    |

  3. a ,b , c are integers, not all simultaneously equal, and omega is cube...

    Text Solution

    |

  4. a, b, c are reals such that a+b+c=3 and   1/(a+b)+ 1/(b+c) + 1/ (c+...

    Text Solution

    |

  5. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

    Text Solution

    |

  6. If alpha,beta are the roots of the quadratic equation a x^2+b x+c=0 , ...

    Text Solution

    |

  7. The locus of z which lies in shaded region (excluding the boundaries) ...

    Text Solution

    |

  8. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

    Text Solution

    |

  9. If a ,b ,c are non-zero real numbers, then find the minimum value of t...

    Text Solution

    |

  10. If z1a n dz2 are two nonzero complex numbers such that =|z1+z2|=|z1|+|...

    Text Solution

    |

  11. if diagonals of a parallelogram bisect each other,prove that its a rho...

    Text Solution

    |

  12. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

    Text Solution

    |

  13. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

    Text Solution

    |

  14. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  15. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

    Text Solution

    |

  16. Referred to the principal axes as the axes of co ordinates find the eq...

    Text Solution

    |

  17. Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot

    Text Solution

    |

  18. sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

    Text Solution

    |

  19. If the equation a x^2+b x+c=0(a &gt;0) has two real roots alphaa n db...

    Text Solution

    |

  20. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<0 b. b c...

    Text Solution

    |