Home
Class 11
MATHS
If z=x+iy and (z-i)/(z+1)is purely imagi...

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

Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAMINATION QUESTION PAPERS 2016

    UNITED BOOK HOUSE|Exercise EXERCISE|51 Videos

  • ANNUAL EXAMINATION QUESTION PAPERS 2018

    UNITED BOOK HOUSE|Exercise EXERCISE|53 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If z=x+iy and w=(1-iz)/(1+iz) such that |w|=1.then show that z is purely real.

If z=x+iyandw=(1-iz)/(z-i) such that |w|=1 , then show that z is purely real.

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), 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.

If z=x+iy and |z-1|+|z+1|=4,then show that 3x^2+4y^2=12 ,where i=sqrt-1

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2017-EXERCISE
  1. If for a triangle ABC , cot A+cotB+cotC=sqrt3,then show that the trian...

    Text Solution

    |

  2. If n in N,then prove by mathematical induction that 7^(2n)+2^3(n-1).3^...

    Text Solution

    |

  3. If z=x+iy and (z-i)/(z+1)is purely imaginary,then show that the point ...

    Text Solution

    |

  4. How many odd numbers of fve digits can be formed with the digits 3,6,7...

    Text Solution

    |

  5. Prove that the middle term in the expansion of (1+x)^(2n)is(1.3.5........

    Text Solution

    |

  6. If the ratio the sum of 1st n terms of two arithemtic series is (4n-13...

    Text Solution

    |

  7. Find the equations of the lines passing thorugh the point (4,5)making ...

    Text Solution

    |

  8. If the equation of the side BC of an equilateral triangle ABC is x+y=2...

    Text Solution

    |

  9. A circle in the first quadrant touches both the axes its centre lies o...

    Text Solution

    |

  10. Evaluate:underset(x rarr 0)(lim)((e^(x)-1)log(1+x))/(sin^(2)x)

    Text Solution

    |

  11. Find from the first principle,the derivative of f(x)=sec2xat x=pi/8.

    Text Solution

    |

  12. Prove by method of contradiction that sqrt5is an irrational number

    Text Solution

    |

  13. Prove that truth table ~(pvq)=~p~q.

    Text Solution

    |

  14. If 30 dates are named at random,find the probability that 5 of them wi...

    Text Solution

    |

  15. calculate the mean deviation about median for the following data:

    Text Solution

    |

  16. Solve: 4 sin x sin 2x sin 4x =sin3x.

    Text Solution

    |

  17. if tan (theta/2)=sqrt((1-e)/(1+e))tan (varphi/2),then prove that cos v...

    Text Solution

    |

  18. Solve the following inequation (|x+2|+2x)/(x+2)>2.

    Text Solution

    |

  19. Solve applying formula: 3x^2-(2-i)x+10-4i=0

    Text Solution

    |

  20. Out of 14 marbles 10 are red in colour and remaining 4 are of differen...

    Text Solution

    |