Home
Class 11
MATHS
If z1,z2,z3 are complex numbers such tha...

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.

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_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 |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

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)| .

If z_1^2+z_2^2+2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

If z_(1)andz_(2) be two non-zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1 , then the origin and the points represented by z_(1)andz_(2)

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

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 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 where lambda in R-{0}, then prove that points corresponding to z_1, z_2 and z_3 are collinear .

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

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |

  2. If alpha,a n dbeta be the roots of the equation x^2+p x-1//2p^2=0,w h ...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  5. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  6. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. ...

    Text Solution

    |

  7. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  8. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^...

    Text Solution

    |

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

    Text Solution

    |

  10. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and...

    Text Solution

    |

  11. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

    Text Solution

    |

  12. If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are t...

    Text Solution

    |

  13. Find the real part of (1-i)^(-i)dot

    Text Solution

    |

  14. The equation (x^2+x+1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will h...

    Text Solution

    |

  15. Convert of the complex number in the polar form: 1-i

    Text Solution

    |

  16. If alpha,beta are the roots of a x^2+c=b x , then the equation (a+c y)...

    Text Solution

    |

  17. If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)

    Text Solution

    |

  18. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

    Text Solution

    |

  19. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

    Text Solution

    |

  20. If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of r...

    Text Solution

    |