Home
Class 11
MATHS
If z be complex no. and (z-1)/(z+1) be p...

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

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    PATHFINDER|Exercise QUESTION BANK|224 Videos

  • CONIC SECTION

    PATHFINDER|Exercise QUESTION BANK|25 Videos

Similar Questions

Explore conceptually related problems

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

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.

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

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

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

If arg ((z-1)/(z+1))=pi/4 ,, then show that in complex plane, the locus of z is a cricle.

If z=3/(2+costheta+isintheta) then show that z lies on a circle in the complex plane

If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex plane is a circle.

Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the complex plane the point z lies on the real axis.

PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

    Text Solution

    |

  2. If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt...

    Text Solution

    |

  3. If x=cosalpha+isinalpha and 1+sqrt(1-y^2)=ny then show that y/2n(1+nx)...

    Text Solution

    |

  4. If a=1/2(5-isqrt3) then find the value of a^3-6a^2+12a-8

    Text Solution

    |

  5. Show that complex numbers (2+i3), (2-i3), (3-i2), (3+i2) are concyclic...

    Text Solution

    |

  6. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

    Text Solution

    |

  7. If z1,z2,z3 are three complex number then prove that z1Im(barz2.z3)+z2...

    Text Solution

    |

  8. Prove that (1-omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)………..to 2n...

    Text Solution

    |

  9. If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...

    Text Solution

    |

  10. If z be complex no. and (z-1)/(z+1) be purely imaginary show that z li...

    Text Solution

    |

  11. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

    Text Solution

    |

  12. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  13. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  14. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

    Text Solution

    |

  15. Ifz1,z2,z3 represent three vertices of an equilateral triangle in arga...

    Text Solution

    |

  16. Prove that the complex numbers z1,z2 and the origin from an isoceles t...

    Text Solution

    |

  17. If (1+x)^n=a0+a1x+a2x^2+…..+anx^n then show that (a0-a2+a4-……)^2+(a1-a...

    Text Solution

    |

  18. If z1,z2,z3………..zn are n complex numbers s.t, abs(z1)=abs(z2)=………….abs...

    Text Solution

    |

  19. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

    Text Solution

    |

  20. If costheta=1/2(a+1/a) cos(phi)=1/2(b+1/b) show that one of the valu...

    Text Solution

    |