Home
Class 12
MATHS
If z(1) and z(2) are the complex roots ...

If `z_(1)` and `z_(2)` are the complex roots of the equation `(x-3)^(3) + 1=0`, then `z_(1) +z_(2)` equal to

A

1

B

3

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
D
`(x-3)^(2)+1=0`
`rArr((x-3)/(-1))^(3)=1`
`rArr (x-3)/(-1)=1,omega,omega^(2)`
`rArr x = 2,3 - omega,3-omega^(2)`
Hence, the sum of complex roots is `6-(omega-omega^(2))=6+1=7`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Multiple)|49 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.11|6 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

If z_(1)andz_(2) are the complex roots of the equation (x-3)^(3)+1=0, then z_(1)+z_(2) equal to 1 b.3 c.5d.7

If z_(1),z_(2),z_(3) andz_(4) are the roots of the equation z^(4)=1, the value of sum_(i=1)^(4)zi^(3) is

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If z_(1),z_(2),z_(3),z_(4) are the roots of equation z^(4)+z^(3)+z^(2)+z+1=0, then prod_(i=1)^(4)(z_(i)+2)

The common roots of the equations z^(3)+2x^(2)+2z+1=0 and z^(2017)+z^(2018)+1=0 are

Sum of common roots of the equations z^(3) + 2z^(2) + 2z + 1 =0 and z^(1985) + z^(100) + 1=0 is

If z_(1),z_(2),z_(3) are any three roots of the equation z^(6)=(z+1)^(6), then arg((z_(1)-z_(3))/(z_(2)-z_(3))) can be equal to

If z_(1),z_(2),z_(3),z_(4) are the roots of the equation z^(4)+z^(3)+z^(2)+z+1=0, then the least value of [|z_(1)+z_(2)|]+1 is (where [.] is GIF.)

CENGAGE-COMPLEX NUMBERS-Exercise (Single)
  1. If z =(lambda+3)+isqrt((5-lambda^2)) ; then the locus of z is

    Text Solution

    |

  2. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

    Text Solution

    |

  3. If z(1) and z(2) are the complex roots of the equation (x-3)^(3) + 1=...

    Text Solution

    |

  4. Which of the following is equal to root(3)(-1)?

    Text Solution

    |

  5. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

    Text Solution

    |

  6. Sum of common roots of the equations z^(3) + 2z^(2) + 2z + 1 =0 and z...

    Text Solution

    |

  7. If 5x^(3) +Mx+ N, M,N in R is divisible by x^(2) + x+1, then the va...

    Text Solution

    |

  8. If z=x+i ya n dx^2+y^2=16 , then the range of ||x|-|y|| is [0,4] b. [0...

    Text Solution

    |

  9. If z is a complex number satisfying the equaiton z^(6) - 6z^(3) + 25 ...

    Text Solution

    |

  10. If 8i z+12 z^2-18 z+27 i=0,t h e n |z|=3/2 b. |z|=2/3 c.|z|=1 d. |z|...

    Text Solution

    |

  11. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  12. |z1|=|z2| and arg((z1)/(z2))=pi, then z1+z2 is equal to

    Text Solution

    |

  13. If for complex numbers z1 and z2, arg(z1) -arg(z2)=0 then |z1-z2| is...

    Text Solution

    |

  14. If |z1/z2|=1 and arg (z1z2)=0 , then

    Text Solution

    |

  15. Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, t...

    Text Solution

    |

  16. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

    Text Solution

    |

  17. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

    Text Solution

    |

  18. If z = (3+ 7i) (a +ib) where a,b in in Z- {0}, is purely imaginary , ...

    Text Solution

    |

  19. If (costheta +isintheta)(cos2theta +isin2theta).....(cosntheta + isinn...

    Text Solution

    |

  20. Given z=(1+isqrt(3))^(100), then [R E(z)//I M(z)] equals 2^(100) b. 2^...

    Text Solution

    |