Home
Class 12
MATHS
Let |(barZ(1) - 2barz(2))//(2-z(1)barz(2...

Let `|(barZ_(1) - 2barz_(2))//(2-z_(1)barz_(2))|= 1` and `|z_(2)| ne 1`, where `z_(1)` and `z_(2)` are complex numbers. shown that `|z_(1)| = 2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|90 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

Let |(z_(1) - 2z_(2))//(2-z_(1)z_(2))|= 1 and |z_(2)| ne 1 , where z_(1) and z_(2) are complex numbers. shown that |z_(1)| = 2

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Complex numbers z satisfy the equaiton |z-(4//z)|=2 Locus of z if |z-z_(1)| = |z-z_(2)| , where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, is

If z_(1) = 1 +iand z_(2) = -3+2i then lm ((z_(1)z_(2))/barz_(1)) is

If z_(1), z_(2) in C (set of complex numbers), prove that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

Prove that |(z-1)/(1-barz)|=1 where z is as complex number.

If k gt 1, |z_(1)| lt k and |(k-z_(1)barz_(2))/(z_(1)-kz_(2))|=1 , then

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

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

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2
  1. If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^...

    Text Solution

    |

  2. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

    Text Solution

    |

  3. Let |(barZ(1) - 2barz(2))//(2-z(1)barz(2))|= 1 and |z(2)| ne 1, where...

    Text Solution

    |

  4. Let z be a complex number having the argument theta ,0 < theta < pi/2,...

    Text Solution

    |

  5. If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...

    Text Solution

    |

  6. If a, b are complex numbers and one of the roots of the equation x^(2)...

    Text Solution

    |

  7. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  8. Find number of values of complex numbers omega satisfying the system o...

    Text Solution

    |

  9. For |z-1|=1, show that tan{[a r g(z-1)]//2}-(2i//z)=-idot

    Text Solution

    |

  10. If nge3and1,alpha(1),alpha(2),.......,alpha(n-1) are nth roots of unit...

    Text Solution

    |

  11. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

    Text Solution

    |

  12. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

    Text Solution

    |

  13. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  14. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

    Text Solution

    |

  15. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  16. If m and x are two real number s and i=sqrt(-1), prove that e^(2mico...

    Text Solution

    |

  17. Find the range of real number alpha for which the equation z + al...

    Text Solution

    |

  18. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

    Text Solution

    |

  19. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  20. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |