Home
Class 11
MATHS
If z1 andz2 be two complex numbers such ...

If `z_1` and`z_2` be two complex numbers such that `abs((z_1-2z_2)/(2-z_1barz_2))=1` and `abs(z_2) ne1`, what is the value of `abs(z_1)` ?

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If z_1 and z_2 be two complex numbers such that abs(z_1+z_2)=abs(z_1) +abs(z_2) then the value of argz_1-argz_2 is equal to

If z_1 and z_2 be two complex numbers such that abszle1, absz_2le1, abs(z_1+iz_2)=abs(z_1-iz_2)=2 , then z_1 equals

If z_1 and z_2 be two complex numbers show that Re(barz_1z_2)=1/2(z_1barz_2+barz_1z_2) where Re(z) is the real part if z .

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

if z_1 and z_2 are two complex numbers such that absz_1lt1ltabsz_2 then prove that abs(1-z_1barz_2)/abs(z_1-z_2)lt1

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

A complex number z is said to be unimodular if absz=1 suppose z_1 and z_2 are complex numbers such that ( z_1-2z_2)/(2-z_1z_2) is unimodular and z_2 in not unimodular then the point z_1 lies on a

Let z_1 and z_2 are two complex nos s.t. abs(z_1) =abs(z_2)=1 then abs((z_1-z_2)/(1-z_1 barz_2)) is equal to

z_1 and z_2 be two complex no. then prove that abs(z_1+z_2)^2+abs(z_1-z_2)^2=2[abs(z_1)^2+abs(z_2)^2]

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. Represent the given complex numbers in polar form : i(1-isqrt3)=i-i^...

    Text Solution

    |

  2. Represent the given complex numbers in polar form : sinalpha-icosalp...

    Text Solution

    |

  3. If z1 andz2 be two complex numbers such that abs((z1-2z2)/(2-z1barz2))...

    Text Solution

    |

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

    Text Solution

    |

  5. Find the square root of -7-24i

    Text Solution

    |

  6. If xr = cos(pi/3^r)+isin (pi/3^r) : prove that x1x2x3....upto infinity...

    Text Solution

    |

  7. if alpha, beta, gamma are roots of x^3-3x^2+3x+7=0, then find (alpha-1...

    Text Solution

    |

  8. If alpha1,alpha2....alpha(n-1) are the nth roots of unity then show th...

    Text Solution

    |

  9. Show that the points represented by complex numbers (3+2i),(2-i),-7i a...

    Text Solution

    |

  10. Find the centre and radius of circle 2absz^2+(3-i)z +(3+i)barz-7=0

    Text Solution

    |

  11. Find all the circles which are orthogonal to absz=1 and abs(z-1)=4

    Text Solution

    |

  12. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

    Text Solution

    |

  13. If 4x+i(3x-y)=3+i(-6), where x and y are real numbers, then find the v...

    Text Solution

    |

  14. Find the multiplicative inverse of 2-3i.

    Text Solution

    |

  15. Convert the complex number (-16)/(1+isqrt3) into polar form.

    Text Solution

    |

  16. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

    Text Solution

    |

  17. Convert the complex number z=(i-1)/(cos(pi/3)+isin(pi/3)) in the polar...

    Text Solution

    |

  18. {1+(-i)^(4n+3)}(1-i), (ninN) equals

    Text Solution

    |

  19. If z1,z2 are conjugate complex numbers and z3,z4 are also conjugate, t...

    Text Solution

    |

  20. If z=(1+i)(1+sqrt 3i)^2/(1-i), then argz equal

    Text Solution

    |