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

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 `(|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^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 x=a+b,y=aomega+bomega^2 and z=aomega^2+bomega , prove that xyz=a^3+b^3

omega is an imaginary root of unity. Prove that If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

If omega be an imaginary cube root of unity, show that (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2

Let omega be the imaginary cube root of unity and (a+bomega + comega^2)^(2015) =(a+bomega^2 + c omega) where a,b,c are unequal real numbers . Then the value of a^2+b^2+c^2-ab-bc-ca equals.

Show that |a b c a+2x b+2y c+2z x y z|=0

If a ,b , c are nonzero real numbers such that |b cc a a b c a a bb c a bb cc 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

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 a^3+b^3+6a b c=8c^3 & omega is a cube root of unity then: (a) a , b , c are in A.P. (b) a , b , c , are in H.P. (c) a+bomega-2comega^2=0 (d) a+bomega^2-2comega=0

If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an imaginary cube root of unity, prove that x^2+y^2+z^2=6ab .

If x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r e .x ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

CENGAGE ENGLISH-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. 71/55

    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 numb...

    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 |z-3-2i|lt=2 then the maximum va...

    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 b...

    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

    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 ,x in Rdot

    Text Solution

    |

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

    Text Solution

    |