Home
Class 12
MATHS
The value of (1+I z +z^(5) + z^(8))^(9)...

The value of `(1+I z +z^(5) + z^(8))^(9)` when `z = (sqrt(3) + i)/(2)` is

A

0

B

`-1`

C

`-i`

D

`(-1 + i)^(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

  • JEE MAIN 2024 ACTUAL PAPER

    JEE MAINS PREVIOUS YEAR|Exercise Question|598 Videos

  • JEE MAINS 2020

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS|250 Videos

Similar Questions

Explore conceptually related problems

If z = (sqrt(5)+3i) , find z^(-1) .

If z=cos((8 pi)/(11))+i sin((8 pi)/(11));i=sqrt(-1) , then the value of Re(z+z^(2)+z^(3)+z^(4)+z^(5)) is lambda , then 20 lambda^(2) is equal to

Suppose z satisfies the equation z^(2) + z + 1 = 0."Let" omega = (z+(1)/(z))^(2) + (z^(2) + (1)/(z^(2)))^(2) + (z^(3) + (1)/(z^(3)))+...+(z^(9) + (1)/(z^(9)))^(2) then |omega + sqrt(301) i| is equal to ____________

If z_(1)= 4-3i and z_(2) = 3 + 9i " then " z_(1) -z_(2) is

If z = 2 + i, prove that z^(3) + 3z^(2) - 9z + 8 = (1 + 14i) .

If z = i(i + sqrt(2)) , then value of z^(4) + 4z^(3) + 6z^(2) + 4z is

JEE MAINS PREVIOUS YEAR-JEE MAINS-Physics
  1. The value of (1+I z +z^(5) + z^(8))^(9) when z = (sqrt(3) + i)/(2) is

    Text Solution

    |

  2. The moment of inertia of a solid sphere, about an axis parallel to its...

    Text Solution

    |

  3. A load of mass M kg is suspended from a steel wire of length 2 m and r...

    Text Solution

    |

  4. In the value circuit, C=(sqrt(3))/(2)muF,R2=20omega, L=sqrt(3)/(10)H, ...

    Text Solution

    |

  5. An ideal gas is enclosed in a cylinder at pressure of 2 atm and temper...

    Text Solution

    |

  6. In the figure, given that V(BB) supply can vary from 0 to 5.0V,V(CC)=5...

    Text Solution

    |

  7. In the circuit shown, find C if the effective capacitance of the whole...

    Text Solution

    |

  8. An alpha-particle of mass m suffers 1-dimentinal eleastic collision wi...

    Text Solution

    |

  9. A 10 m long horizontal wire extends from North east ro South East. It ...

    Text Solution

    |

  10. To double the covering range of a TV transmittion tower, its height sh...

    Text Solution

    |

  11. A plano-convex lens (focal length f2, refractive indexmu(2), radius of...

    Text Solution

    |

  12. A vertical closed cylinder is separated into two parts by a frictionle...

    Text Solution

    |

  13. Two satellites, A and B, have masses m and 2m respectively. A is in a ...

    Text Solution

    |

  14. A long cylinderical vessel is half filled with a liquid. When the vess...

    Text Solution

    |

  15. A block kept on a rough inclined plane ,as shown in the figure, remain...

    Text Solution

    |

  16. In a Frank-Hertz experiment,an electron of energy 5.6eV passes through...

    Text Solution

    |

  17. A particle of mass 20 g is released with an initial velocity 5m//s alo...

    Text Solution

    |

  18. A galavanometer, whose resistance is 50 ohm has 25 divisions in it. Wh...

    Text Solution

    |

  19. A soap bubble,blown by a mechanical pump at the mouth of a tube, incre...

    Text Solution

    |

  20. In the given circuit diagram, the currents, I1=-0.3A,I4=0.8A and I5=0....

    Text Solution

    |

  21. A resonance tube is old and has jagged end. It is still used in the la...

    Text Solution

    |