Home
Class 12
MATHS
Show that the equation of the circle in ...

Show that the equation of the circle in the complex plane with `z_1 & z_2` as its diameter can be expressed as , `2z barz-(barz_1+barz_2)z-(barz_1+barz_2)barz+z_1barz_2+z_2barz_1=0`

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

Find the complex number z if z^2+barz =0

Find the complex number z if zbarz = 2 and z + barz=2

Solve the equation z^(3) = barz (z ne 0)

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

If z_(1) = 3+ 2i and z_(2) = 2-i then verify that (i) bar(z_(1) + z_(2)) = barz_(1) + barz_(2)

Solve: z +2barz=ibarz

Prove that equation of perpendicular bisector of line segment joining complex numbers z_(1) and z_(2) is z(barz_(2) - barz_(1)) + barz (z_(2) + z_(1)) + |z_(1)|^(2) -|z_(2)|^(2) =0

Let A(z_1), B(z_2) and C(z_3) forms an acute angled triangle in argand plane having origin as it’s orthocentre. Prove that z_1barz_2+bar(z)_1 z_2=z_2barz_3+barz_2z_3=z_3barz_1 +barz_3z_1

Which of the following is (are) correct? (A) barz_1+abarz_2=2b (B) barz_1+abarz_2=b (C) barz_1+abarz_2=-b (D) barz_1+abarz_2=-2b

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Show that the equation of the circle in the complex plane with z1 & z2...

    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

    |