Home
Class 12
MATHS
If z^2+z+1=0 where z is a complex number...

If `z^2+z+1=0` where `z` is a complex number, then the value of `(z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2` is

A

18

B

54

C

6

D

12

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 7|11 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

If z is any complex number, prove that : |z|^2= |z^2| .

If z is a complex number such that |z|geq2 , then the minimum value of |z+1/2|

For any complex number z, the minimum value of |z|+|z-1| is :

Solve that equation z^2+|z|=0 , where z is a complex number.

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .

If |z|=1 and z!=1, then all the values of z/(1-z^2) lie on

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1/z_2|= (|z_1|)/ (|z_2|), z_2 ne 0 .

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .

If z_1, z_2 are two complex numbers satisfying the equation |(z_1 +z_2)/(z_1 -z_2)|=1 , then z_1/z_2 is a number which is :

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

    Text Solution

    |

  2. Find the value of sum(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wher...

    Text Solution

    |

  3. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

    Text Solution

    |

  4. A man walks a distance of 3 units from the origin towards the North-...

    Text Solution

    |

  5. If |z|=1 and z!=1, then all the values of z/(1-z^2) lie on

    Text Solution

    |

  6. If abs(z+4) le 3, the maximum value of abs(z+1) is

    Text Solution

    |

  7. Let A, B, C be three sets of complex number as defined below: A={z:Img...

    Text Solution

    |

  8. What is 5% Equals to

    Text Solution

    |

  9. Express in the form of complex number i^9+i^(19)

    Text Solution

    |

  10. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

    Text Solution

    |

  11. If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...

    Text Solution

    |

  12. Let z = x + iy be a complex number where x and y are integers. Then...

    Text Solution

    |

  13. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1...

    Text Solution

    |

  14. If |z-4/z|=2 then the greatest value of |z| is:

    Text Solution

    |

  15. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

    Text Solution

    |

  16. Find the value of 2^4

    Text Solution

    |

  17. If alpha and beta are the roots of the equation x^2"-"x""+""1""=""0 , ...

    Text Solution

    |

  18. The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

    Text Solution

    |

  19. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  20. The set {R e((2i z)/(1-z^2)): z is a complex number,|z|=1,z=+-1} is.

    Text Solution

    |