Home
Class 11
MATHS
A complex number z is said to be unimodu...

A complex number z is said to be unimodular if `absz=1` suppose `z_1` and `z_2` are complex numbers such that `( z_1-2z_2)/(2-z_1z_2)` is unimodular and `z_2` in not unimodular then the point `z_1` lies on a

A

straight line parallel to y axis

B

circle of radius 2

C

circle of radius `sqrt2`

D

straight line parallel to x axis

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

A complex number z is said to be unimodular if |z|=1 Suppose z_(1)andz_(2) are complex number such that (z_(1)-^(2z)2)/(2-z_(1)z_2) is unimodular and z_(2) is not unimodular .Then the point z_(1) lies on a -

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If z_1 and z_2 be two complex numbers such that abs((z_1-2z_2)/(2-z_1barz_2))=1 and abs(z_2) ne1 , what is the value of abs(z_1) ?

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

If z_1 and z_2 be two complex numbers such that abs(z_1+z_2)=abs(z_1) +abs(z_2) then the value of argz_1-argz_2 is equal to

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

If z_1,z_2 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are

If z_1, z_2 are complex number such that (2z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/(z_1+z_2)| .

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z_1 and z_2 be two complex numbers show that Re(barz_1z_2)=1/2(z_1barz_2+barz_1z_2) where Re(z) is the real part if z .

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. Let omega ne1 be a complex cube root of unity if (3-3omega+2omega^2)^(...

    Text Solution

    |

  2. For any integer k let alphak=cos((kpi)/7)+isin((kpi)/7) where i=sqrt(-...

    Text Solution

    |

  3. A complex number z is said to be unimodular if absz=1 suppose z1 and z...

    Text Solution

    |

  4. The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

    Text Solution

    |

  5. Find the maximum value of absz when abs(z-3/z)=2 ,z being a complex nu...

    Text Solution

    |

  6. If z is a complex number such that abszge2 then the minimum value of a...

    Text Solution

    |

  7. Let z1,z2 be two fixed complex numbers in the Argand plane and z be an...

    Text Solution

    |

  8. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

    Text Solution

    |

  9. Suppose that z1, z2, z3 are three vertices of an equilateral triangle ...

    Text Solution

    |

  10. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

  11. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

    Text Solution

    |

  12. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

    Text Solution

    |

  13. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

    Text Solution

    |

  14. If z is a complex number of unit modulus and argument theta then arg(...

    Text Solution

    |

  15. Let z1=2+3i and z2=3+4i be two points on the complex plane then the se...

    Text Solution

    |

  16. Suppose z=x+iy where x and y are real numbers and i=sqrt(-1) the point...

    Text Solution

    |

  17. If P,Q,R are angles of an isosceles triangle and anglep=pi/2 then the ...

    Text Solution

    |

  18. Let z be a complex number such that the imaginary part of z is non zer...

    Text Solution

    |

  19. If z ne 1 and (z^2)/(z-1) is real then the point represented by the co...

    Text Solution

    |

  20. The maximum value of absz when the complex number z satisfies the cond...

    Text Solution

    |