Home
Class 12
MATHS
Let w = (sqrt 3 + iota/2) and P = { w^n ...

Let w = (`sqrt 3 + iota/2)` and `P = { w^n : n = 1,2,3, ..... },` Further `H_1 = { z in C: Re(z) > 1/2} and H_2 = { z in c : Re(z) < -1/2}` Where C is set of all complex numbers. If `z_1 in P nn H_1 , z_2 in P nn H_2` and O represent the origin, then `/_Z_1OZ_2` =

A

`pi/2`

B

`pi/6`

C

`(2pi)/3`

D

`(5pi)/6`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

Let w=(sqrt(3)+(iota)/(2)) and P={w^(n):n=1,2,3,....}, Further H_(1)={z in C:Re(z)>(1)/(2)} and H_(2)={z in c:Re(z)<-(1)/(2)} Where C is set of all complex numbers.If z_(1)in P nn H_(1),z_(2)in P nn H_(2) and O represent the origin,then /_Z_(1)OZ_(2)=

Let S=S_(1)nn S_(2)nn S_(3), where s_(1)={z in C:|z| 0} and S_(3)={z in C:Re z>0

For all complex number z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2)-3-4 iota|=5, then |z_(2)-iota z_(1)|

If the points represented by complex numbers z_(1)=a+ib, z_(2)=c+id " and " z_(1)-z_(2) are collinear, where i=sqrt(-1) , then

If z_1=a+ib and z_2=c+id are two complex numbers then z_1 gt z_2 is meaningful if

The set {Re((2iz)/(1-z^(2))):z is a complex number,|z|=1,z=+-1}

Let |z|=2 and w-(z+1)/(z-1), where z,w,in C (where C is the set of complex numbers).Then product of least and greatest value of modulus of w is

Let C be the set of all complex numbers. Let S_(i) = {z in C||z-3-2i|^(2)=8}, S_(2)= {z in C|Re (z) ge 5} and S_(3)= {z in C||z-bar(z)| ge 8} . Then the number of elements in S_(1) nn S_(2) nn S_(3) is equal to

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Match the statement in Column I with those in Column II. [Note : He...

    Text Solution

    |

  2. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

    Text Solution

    |

  3. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  4. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

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

    Text Solution

    |

  6. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  7. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |

  8. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  9. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

    Text Solution

    |

  10. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

    Text Solution

    |

  11. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

    Text Solution

    |

  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  14. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

    Text Solution

    |

  15. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  16. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

    Text Solution

    |

  17. Let P=[{:((-z)^r,z^(2r)),(z^(2r),z^r):}] and Ibe the identity matrix o...

    Text Solution

    |

  18. Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the co...

    Text Solution

    |

  19. Let s ,\ t ,\ r be non-zero complex numbers and L be the set of ...

    Text Solution

    |

  20. For a non-zero complex number z , let arg(z) denote the principal ar...

    Text Solution

    |