Home
Class 12
MATHS
If x=a+b,y=a alpha+b beta and z=abeta+ ...

If `x=a+b,y=a alpha+b beta and z=abeta+ b alpha` , where `alpha and beta` are the imaginary cube roots ofunity, then `xyz=`

A

` 2 ( a^(3) + b^(3)+ c^(3))`

B

` 2 ( a^(3) -b^(3) -c^(3))`

C

` a^(3) +b^(3) -c^(3)-3abc`

D

` a^(3) -b^(3) -c^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|50 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

If x=a + b, y= a alpha + b beta, z= a beta + b alpha , where alpha and beta are complex cube roots of unity, then show that xyz = a^(3) + b^(3)

If x = a + b , y = a alpha + b beta , z = a beta + b alpha where alpha and beta are complex cube roots of unity , show that x^(3) +y^(3) + z^(3) = 3 (a^(3)+ b^(3))

Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , where alpha and beta are the roots of the equation x^(2)+2x+3=0 .

If alpha , beta , gamma in {1,omega,omega^(2)} (where omega and omega^(2) are imaginery cube roots of unity), then number of triplets (alpha,beta,gamma) such that |(a alpha+b beta+c gamma)/(a beta+b gamma+c alpha)|=1 is

If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta , prove that acosbeta=bcosalphadot

If 0 gt a gt b gt c and the roots alpha, beta are imaginary roots of ax^(2) + bx + c = 0 then

(i) If alpha , beta be the imaginary cube root of unity, then show that alpha^4+beta^4+alpha^-1beta^-1=0

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

If 0 lt c lt b lt a and the roots alpha, beta the equation cx^(2)+bx+a=0 are imaginary, then

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 1
  1. If z and w are two non-zero complex numbers such that z=-w.

    Text Solution

    |

  2. The square roots of - 2 + 2 sqrt(3)i are :

    Text Solution

    |

  3. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  4. If a = cos 2 alpha + i sin 2 alpha , b= cos 2 beta + i sin 2 beta , ...

    Text Solution

    |

  5. The complex number 2^n/(1+i)^(2n)+(1+i)^(2n)/2^n , n epsilon I is equa...

    Text Solution

    |

  6. If z1=9y^2-4-10 i x ,z2=8y^2-20 i ,w h e r ez1=( z )2, then find z=x+...

    Text Solution

    |

  7. The square roots of 7+24i are

    Text Solution

    |

  8. If omega is a complex cube root of unity then (1-omega+omega^2)(1-omeg...

    Text Solution

    |

  9. If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3, , prove that z1z2z3 zoo=idot

    Text Solution

    |

  10. If omega is a complex cube roots of unity, then find the value of the...

    Text Solution

    |

  11. The value of (4(cos75^(@) + isin 75^(@)))/(0.4(cos30^(@) + i sin 30^(...

    Text Solution

    |

  12. If z = cos alpha + i sin alpha then the amplitude of z^2+barz is:

    Text Solution

    |

  13. if (1+i)z=(1-i)barz then z is

    Text Solution

    |

  14. If arg ( z - 1) = arg (z + 3i), then find x - 1 : y, where z = x + iy ...

    Text Solution

    |

  15. If x^2-x+1=0 then the value of sum[n=1]^[5][x^n+1/x^n]^2 is:

    Text Solution

    |

  16. If omega is a complex cube root of unity, then ((1+i)^(2n)-(1-i)^(2n))...

    Text Solution

    |

  17. If the fourth roots of unity are z1, z2, z3, z4 and z1^2+z2^2+z3^2+z4^...

    Text Solution

    |

  18. If z is nanreal root of ""^(7)sqrt(-1), then find the value of z ^(86...

    Text Solution

    |

  19. The angle that the vector representing the complex number 1/(sqrt3-i)...

    Text Solution

    |

  20. If omega is a complex cube root of unity, then value of expression cos...

    Text Solution

    |