Home
Class 11
MATHS
If (z-1)/(z+1) is purely imaginary then...

If (z-1)/(z+1) is purely imaginary then

A

`absz=1/2`

B

`absz=1`

C

`absz=2`

D

`absz=3`

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

If z is a complex number such that (z-1)/(z+1) is purely imaginary, then the value of |z| is-

If z=x+iy and (z-i)/(z+1) is purely imaginary,then show that the point z always lies on a circle.

If z=x+iyand(z-i)/(z+1) is purely imaginary, then show that the point z always lies on a circle.

Let z=x+iy , where x and y are real. The points (x,y) in the xy-plane of which (z+1)/(z-1) is purely imaginary, lie on

If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

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 (z_1!=z_2) satisfying |z_1^2-z_2^2|=| z_ 1^2+ z _2 ^2-2( z _1)( z _2)| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

If z=x+iy and |z|=1 , show that (z-1)/(z+1)(z!=-1) is a purely imaginary quantity.

P(z_1),Q(z_2),R(z_3)a n dS(z_4) are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? (z_1-z_4)/(z_2-z_3) is purely real a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4) (z_1-z_3)/(z_2-z_4) is purely imaginary It is not necessary that |z_1-z_3|!=|z_2-z_4|

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If (3/2+isqrt3/2)^50=3^25(x+iy)where x and y are real then the order P...

    Text Solution

    |

  13. If (z-1)/(z+1) is purely imaginary then

    Text Solution

    |

  14. The points representing the complex number z for which arg((z-2)/(z+2)...

    Text Solution

    |

  15. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  16. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |

  17. If omega(ne1) is a cube root of unity and (1+omega)^7=A+Bomega then (A...

    Text Solution

    |

  18. For the real parameter t,the locus of the complex number z=(1-t^2)+isq...

    Text Solution

    |

  19. If x+(1/x)=2costheta then for any integer n,x^n+1/x^n=

    Text Solution

    |

  20. If omega ne1 is a cube root of unity then the sum of the series S=1+2o...

    Text Solution

    |