Home
Class 12
MATHS
If z=(sqrt(3)-i)/2, where i=sqrt(-1), th...

If `z=(sqrt(3)-i)/2`, where `i=sqrt(-1)`, then `(i^(101)+z^(101))^(103)` equals to

A

iz

B

z

C

`bar(z)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|12 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise For Session 4|14 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=(sqrt(3+i))/(2)( where i=sqrt(-1)) then (z^(101)+i^(103))^(105) is equal to

If z= (sqrt3-i)/2 , " then " (i^(101)+z^(101))^(103) erqual

If z=i^(i) where i=sqrt(-)1 then |z| is equal to

If i=sqrt(-1) , then {i^(n)+i^(-n), n in Z} is equal to

If z=sqrt(2i), then z is equal to

Let z_(1),z_(2) and z_(3) be non-zero complex numbers satisfying z^(2)=bar(iz), where i=sqrt(-1). What is z_(1)+z_(2)+z_(3) equal to ?

If 8iz^(3)+12z^(2)-18z+27i=0, (where i=sqrt(-1)) then

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Single Option Correct Type Questions)
  1. If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0, where i=sqrt(-1), then z bar...

    Text Solution

    |

  2. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

    Text Solution

    |

  3. If z=(sqrt(3)-i)/2, where i=sqrt(-1), then (i^(101)+z^(101))^(103) equ...

    Text Solution

    |

  4. Let alpha and beta be two fixed non-zero complex numbers and 'z' a var...

    Text Solution

    |

  5. If alpha = cos((8pi)/11)+i sin ((8pi)/11) then Re(alpha + alpha^2+alph...

    Text Solution

    |

  6. The set of points in an Argand diagram which satisfy both abs(z)le4 an...

    Text Solution

    |

  7. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

    Text Solution

    |

  8. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

    Text Solution

    |

  9. Let C and R denote the set of all complex numbers and all real numb...

    Text Solution

    |

  10. Let alpha and beta be two distinct complex numbers, such that abs(alph...

    Text Solution

    |

  11. The complex number z satisfies thc condition |z-25/z|=24. The maximum ...

    Text Solution

    |

  12. The points A,B and C represent the complex numbers z(1),z(2),(1-i)z(1)...

    Text Solution

    |

  13. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

    Text Solution

    |

  14. Dividing f(z) by z-i, we obtain the remainder 1-i and dividing it by z...

    Text Solution

    |

  15. The centre of circle represented by |z + 1| = 2 |z - 1| in the complex...

    Text Solution

    |

  16. If x=9^(1/3) 9^(1/9) 9^(1/27) ......ad inf y= 4^(1/3) 4^(-1/9) 4^(1/...

    Text Solution

    |

  17. If centre of a regular hexagon is at origin and one of the vertices on...

    Text Solution

    |

  18. Let |Z(r) - r| le r, Aar = 1,2,3….,n. Then |sum(r=1)^(n)z(r)| is less ...

    Text Solution

    |

  19. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

    Text Solution

    |

  20. If abs(z-2-i)=abs(z)abs(sin(pi/4-arg"z")), where i=sqrt(-1), then locu...

    Text Solution

    |