Home
Class 11
MATHS
Let omega=e^(ipi/3),and a,b,c,x,y,z be n...

Let `omega=e^(ipi/3)`,and a,b,c,x,y,z be non zero complex numbers such that `a+b+c=x`
`a+bomega+comega^2=y`
`a+bomega^2+comega=z` then the value of `(absx^2+absy^2+absz^2)/(absa^2+absb^2+absc^2)` is

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If x=a+b , y=aomega+bomega^2 , z=aomega^2+bomega then show that , x^3+y^3+z^3=3(a^3+b^3)

prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc if a+b+c=0.

If z(Re z ne2) be a complex number such that z^2-4z=absz^2+16/absz^3 then the value of absz^4 is

If omega is the imaginary cube root of unity and a+b+c=0 then show that (a+bomega+comega^2)^3+(a+bomega^2+comega)^3=27abc

Let x , y , z be non - zero real numbers lying in the interval [-1,1] such that cos^-1 x + cos^-1 y + cos^-1 z = pi The value of x sqrt(1 - x^2) + ysqrt(1 - y^2) + zsqrt(1 - z^2) is equal to

If omega is an imaginary cube root of unity , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a+b+c)(a+bomega+comega^2)(a+bomega^2+comega)

If omega is the imaginary cube root of 1 then prove that (a+bomega+comega^2)^3+(a+bomega^2+comega)^3 = (2a-b-c)(2b-a-c)(2c-a-b)

If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, a b,b c],[ a b,b c,c a]|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x=1+1/(3+1/(2+1/(3+1/(2)))) a 52/2 b. 55/71 c. 60/52 d....

    Text Solution

    |

  2. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

    Text Solution

    |

  3. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |

  4. Find the values of a for which all the roots of the euation x^4-4x^3-8...

    Text Solution

    |

  5. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  6. Let |(( bar z 1)-2( bar z 2))//(2-z1( bar z 2))|=1 and |z2|!=1,where z...

    Text Solution

    |

  7. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 ...

    Text Solution

    |

  8. Let 1,w,w^2 be the cube root of unity. The least possible degree of a ...

    Text Solution

    |

  9. If z1a n dz2 are complex numbers and u=sqrt(z1z2) , then prove that |z...

    Text Solution

    |

  10. The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a....

    Text Solution

    |

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

    Text Solution

    |

  12. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

    Text Solution

    |

  13. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 ...

    Text Solution

    |

  14. Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z ...

    Text Solution

    |

  15. (costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

    Text Solution

    |

  16. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  17. Identify locus z if R e(z+1)=|z-1|

    Text Solution

    |

  18. If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of...

    Text Solution

    |

  19. Solve the equation sqrt(a(2^x-2)+1)=1-2^x for every value of the param...

    Text Solution

    |

  20. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the va...

    Text Solution

    |