Home
Class 12
MATHS
If z ne 1 and (z^(2))/(z-1) is real, the...

If `z ne 1` and `(z^(2))/(z-1)` is real, the point represented by the complex numbers z lies

A

on a circle with centre at the origin.

B

either on the real axis or on a circle not passing through the origin.

C

on the imaginary axis.

D

either on the real axis or on a circle passing through the origin

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE NUMERICAL ANSWER TYPE QUESTIONS|20 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

If z!=1 and (z^2)/(z-1) is real, then the point represented by the complex number z lies (1) either on the real axis or on a circle passing through the origin (2) on a circle with centre at the origin (3) either on the real axis or on a circle not passing through the origin (4) on the imaginary axis

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=2 then the points representing the complex number -1+5z will be

If the real part of (z+2)/(z-1) is 4, then show that the locus of he point representing z in the complex plane is a circle.

Let A, B, C represent the complex numbers z_1, z_2, z_3 respectively on the complex plane. If the circumcentre of the triangle ABC lies at the origin, then the orthocentre is represented by the complex number

The point representing the complex number z for which arg (z-2)(z+2)=pi/3 lies on

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
  1. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

    Text Solution

    |

  2. Let alpha,beta be real and z be a complex number. If z^2+alphaz""+beta...

    Text Solution

    |

  3. If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...

    Text Solution

    |

  4. The area of the triangle on the Arand plane formed by the complex numb...

    Text Solution

    |

  5. If z is a complex number of unit modulus of modulus and argument thet...

    Text Solution

    |

  6. if (5z2)/(7z1) is purely imaginary number then |(2z1+3z2)/(2z1-3z2) |...

    Text Solution

    |

  7. Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...

    Text Solution

    |

  8. If a complex number z satisfies z + sqrt(2) |z + 1| + i=0, then |z| is...

    Text Solution

    |

  9. If z is a complex number such that |z|>=2 then the minimum value of |z...

    Text Solution

    |

  10. Let w(Im w != 0) be a complex number. Then the set of all complex num...

    Text Solution

    |

  11. If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...

    Text Solution

    |

  12. Let z!=i be any complex number such that (z-i)/(z+i) is a purely imagi...

    Text Solution

    |

  13. For all complex numbers z of the form 1 + ialpha, alpha in "R if z"^(2...

    Text Solution

    |

  14. A complex number z is said to be uni-modular if |z|=1. Suppose z(1) a...

    Text Solution

    |

  15. The largest value of r for which the region represented by the set {om...

    Text Solution

    |

  16. If Z is a non-real complex number, then find the minimum value of (Imz...

    Text Solution

    |

  17. A value of for which (2+3isintheta)/(1-2isintheta) purely imaginary, ...

    Text Solution

    |

  18. The point represented by 2+i in the Argand plane moves 1 unit eastward...

    Text Solution

    |

  19. Let z=1+ai be a complex number, a > 0,such that z^3 is a real number....

    Text Solution

    |

  20. Let zinC, the set of complex numbers. Thenthe equation, 2|z +3i| - |z...

    Text Solution

    |