Home
Class 12
MATHS
if z = (sqrt 3 ) /(2) + (i)/(2) ( ...

if ` z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) )`, then ` ( 1 + iz + z^5 + iz^8)^9 ` is equal to:

A

0

B

1

C

`(-1 + 2i)^(9)`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 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=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

If z= -3 + sqrt2i , then prove that z^(4) + 5z^(3) + 8z^(2) + 7z + 4 is equal to -29

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

If z = (-4 +2 sqrt3i)/(5 +sqrt3i) , then the value of arg(z) is

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

If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=0.

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

If z=re^(itheta) then |e^(iz)| is equal to:

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

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

    Text Solution

    |

  2. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

    Text Solution

    |

  5. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

    Text Solution

    |

  6. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

    Text Solution

    |

  7. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

    Text Solution

    |

  8. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

    Text Solution

    |

  9. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

    Text Solution

    |

  10. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

    Text Solution

    |

  11. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

    Text Solution

    |

  12. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

    Text Solution

    |

  13. Let z in c be such that |z| lt . If omega = (5 + 3z)/(5(1 - z)), then ...

    Text Solution

    |

  14. If z = ((1+i)^(2))/(alpha-i), alpha in R has magnitude sqrt((2)/(5)) ...

    Text Solution

    |

  15. Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=p...

    Text Solution

    |

  16. The equation |z-1|=|z+1|,i= sqrt(-1)represents =

    Text Solution

    |

  17. if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

    Text Solution

    |

  18. if z is a complex number belonging to the set S={z:|z-2+i|gesqrt(5)} a...

    Text Solution

    |

  19. Let alpha and beta are roots of equation x^(2)-x-1=0 with alpha > bet...

    Text Solution

    |

  20. If omega is a cube root of unity but not equal to 1, then minimum valu...

    Text Solution

    |