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

` barz`

D

`omegaz, (omega ` is complex cube root of unity)

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -C) (objective Type Questions ( more thena one options are correct )|35 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -D) Linked comprehension Type Questions|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 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 i=sqrt(-1) , then (i^(n)+i^(-n), n in Z) is equal to

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

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

If z=(3-sqrt(7)i) , then find |z^(-1)| .

If z(2-2sqrt(3i))^2=i(sqrt(3)+i)^4, then a r g(z)=

If z=i log(2-sqrt(3)) then cosz

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

sqrt((-8-6i)) is equal to (where, i=sqrt(-1)

If z=ilog_(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

    Text Solution

    |

  2. If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omeg...

    Text Solution

    |

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

    Text Solution

    |

  4. The region of the complex plane for which |(z-a)/(z+veca)|=1,(Re(a) !=...

    Text Solution

    |

  5. If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the loc...

    Text Solution

    |

  6. In z is a complex number stisfying |2008z-1|= 2008|z-2|, then locus z ...

    Text Solution

    |

  7. The locus of the points z satisfying the condition arg ((z-1)/(z+1))=p...

    Text Solution

    |

  8. the locus of z=i+2exp(i(theta+pi/4)) is

    Text Solution

    |

  9. If one vertex and centre of a square are z and origin then which of th...

    Text Solution

    |

  10. if the complex no z1 , z2 and z3 represents the vertices of an equ...

    Text Solution

    |

  11. If |z-2-3i|+|z+2-6i|=4where i=sqrt(-1),then locus of P (z) is

    Text Solution

    |

  12. If z(1),z(2),z(3) and u,v,w are complex numbers represending the verti...

    Text Solution

    |

  13. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

    Text Solution

    |

  14. For two complex numbers z(1) and z(2) , we have |(z(1)-z(2))/(1-barz(1...

    Text Solution

    |

  15. Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

    Text Solution

    |

  16. If the ratio of the roots of the equation lx^2+nx+n=0 is p:q prove tha...

    Text Solution

    |

  17. For the equation |x^(2)| + |x| -6=0, the roots are

    Text Solution

    |

  18. If a+b+c=0 and a,b,c are rational. Prove that the roots of the equatio...

    Text Solution

    |

  19. If secalpha, tanalpha are roots of ax^2 + bx + c = 0, then

    Text Solution

    |

  20. If x is real then the values of (x^(2) + 34 x - 71)/(x^(2) + 2x - 7) d...

    Text Solution

    |