Home
Class 12
MATHS
Prove that the equations , |(z-1)/(z+1)|...

Prove that the equations , `|(z-1)/(z+1)|` = constant and amp `((z-1)/(z+1))` = constant on the argand plane represent the equations of the circle wich are orthogonal .

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 1 (OBJECTIVE PROBLEMS I JEE MAIN) - SECTIONS - A & B|4 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 1 (OBJECTIVE PROBLEMS I JEE MAIN) - SECTIONS - C|1 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

The equation |z - i| = |z - 1| represents :

In the Argand plane |(z-i)/(z+i)| = 4 represents a

The equation |z-1|^(2)+|z+1|^(2)=2 , represent

The locus represented by the equation |z-1|=|z-i| is

The locus represented by the equation |z-1|=|z-i| is

Find all circles which are orthogonal to |z|=1and|z-1|=4.

If z is a comlex number in the argand plane, the equation |z-2|+|z+2|=8 represents

If z^4= (z-1)^4 then the roots are represented in the Argand plane by the points that are

The locus represented by the equat ion,|z-1|+|z+1|=2 is

Q.2 The equation |z+1-i|=|z+i-1| represents a

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Prove that the equations , |(z-1)/(z+1)| = constant and amp ((z-1)/(z...

    Text Solution

    |

  2. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

    Text Solution

    |

  3. A man walks a distance of 3 units from the origin towards the North...

    Text Solution

    |

  4. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

    Text Solution

    |

  5. A particle P starts from the point z(0)=1+2i, where i=sqrt(-1). It mov...

    Text Solution

    |

  6. Let A ,B ,C be three sets of complex number as defined below A={z : I ...

    Text Solution

    |

  7. Let A,B,C be three sets of complex number as defined below A={z:lm ...

    Text Solution

    |

  8. Let A,B,C be three sets of complex number as defined below A={z:lm ...

    Text Solution

    |

  9. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

    Text Solution

    |

  10. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1)) ...

    Text Solution

    |

  11. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  12. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  13. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |

  14. Let omega be the complex number " cos " ( 2pi)/(3) + isin (2pi)/(3)...

    Text Solution

    |

  15. Match the statement in Column I with those in Column II. [Note : He...

    Text Solution

    |

  16. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

    Text Solution

    |

  17. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  18. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  19. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  20. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  21. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |