Home
Class 11
MATHS
If z1, z2 are complex number such that (...

If `z_1, z_2` are complex number such that `(2z_1)/(3z_2)` is purely imaginary number, then find `|(z_1-z_2)/(z_1+z_2)|` .

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

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

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

Let z_1 and z_2 be complex numbers such that z_1 nez_2 and absz_1=absz_2 if z_1 has positive real part then (z_1+z_2)/(z_1-z_2) may be

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

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

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

z_(1) and z_(2)( ne z_(1)) are two complex numbers such that |z_(1)|=|z_(2)| . Sho that the real part of (z_(1)+z_(2))/(z_(1)-z_(2)) is zero.

If z_1,z_2 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are

If z_1,z_2,z_3 are complex numbers such that 2/z_1=1/z_2 + 1/z_3 , show that the points represented by z_1,z_2,z_3 lie on a circle passing through the origin.

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

    Text Solution

    |

  2. The set of all possible real values of a such that the inequality (x-(...

    Text Solution

    |

  3. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |

  4. The interval of a for which the equation t a n^2x-(a-4)tanx+4-2a=0 has...

    Text Solution

    |

  5. The range of a for which the equation x^2+ax-4=0 has its smaller root ...

    Text Solution

    |

  6. Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 ...

    Text Solution

    |

  7. Consider the equation x^2+2x-n=0 where n in N and n in [5,100] The t...

    Text Solution

    |

  8. (1+i)^(n1)+(1+i^3)^(n1)+(1+i^5)^(n2)+(1+i^7)^(n2) is a real number if

    Text Solution

    |

  9. The total number of values a so that x^2-x-a=0 has integral roots, wh...

    Text Solution

    |

  10. If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is ...

    Text Solution

    |

  11. Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and wi...

    Text Solution

    |

  12. If a r g(z)<0, then a r g(-z)-"arg"(z) equals pi (b) -pi (d) -pi/2 ...

    Text Solution

    |

  13. Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniq...

    Text Solution

    |

  14. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

    Text Solution

    |

  15. if a lt c lt b, then check the nature of roots of the equation (a ...

    Text Solution

    |

  16. Let z1 and z2 be the nth roots of unity which subtend a right angle at...

    Text Solution

    |

  17. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

  18. The complex numbers z1,z2 and z3 satisfying (z1-z3)/(z2-z3)=(1-isqrt3)...

    Text Solution

    |

  19. The value of a so that the sum of the squares of the roots of the equa...

    Text Solution

    |

  20. For all complex niumbers z1, z2 satisfying absz1=12 and abs(z2-3-4i)=5...

    Text Solution

    |