Home
Class 12
MATHS
If z = x + iy and arg ((z-1)/(z+1))=pi/2...

If z = x + iy and arg `((z-1)/(z+1))=pi/2`, show that `x^(2)+y^(2)-1=0`.

Text Solution

Verified by Experts

The correct Answer is:
`x^2 + y^2 = 1`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED|59 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.1|6 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

If z = x + iy and arg ((z - i)/(z + 2))= (pi)/(4) . Show that x^(2) + y^(2) + 3x - 3y + 2 = 0 .

If arg(z - 1) = pi/6 and arg(z + 1) = 2 pi/3 , then prove that |z| = 1 .

If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then find zdot

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1

If z = + iy is complex number such that Im ((2z + 1)/(iz + 1)) = 0, show that the locus of z is 2x^(2) + 2y^(2) + x - 2y = 0.

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi, show that x + y + z = xyz.

FULL MARKS-COMPLEX NUMBERS -EXERCISE - 2.9
  1. If z = x + iy and arg ((z-1)/(z+1))=pi/2, show that x^(2)+y^(2)-1=0.

    Text Solution

    |

  2. i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)

    Text Solution

    |

  3. The value of sum(i=1)^(13) (n^(n) + i^(n-1)) is

    Text Solution

    |

  4. The area of the triangle formed by the complex numbers z, iz, and z + ...

    Text Solution

    |

  5. The conjugate of a complex number is (1)/(i-2). Then, the complex numb...

    Text Solution

    |

  6. If z= ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)), then |z| is equal...

    Text Solution

    |

  7. If z is non zero complex number, such that 2i z^(2) = bar(z),then |z| ...

    Text Solution

    |

  8. If |z-2 + i|le2, then the greatest value of |z| is

    Text Solution

    |

  9. If |z - (3)/(z)| = 2, then the least value of |z| is

    Text Solution

    |

  10. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

    Text Solution

    |

  11. The solution of the equation |z| -z = 1 + 2i is

    Text Solution

    |

  12. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

    Text Solution

    |

  13. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

    Text Solution

    |

  14. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

    Text Solution

    |

  15. If (z - 1)/(z + 1) is purely imaginary, then |z| is

    Text Solution

    |

  16. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

    Text Solution

    |

  17. The principal argument of (3)/(-1 + i) is

    Text Solution

    |

  18. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

    Text Solution

    |

  19. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

    Text Solution

    |

  20. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

    Text Solution

    |

  21. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

    Text Solution

    |