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

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

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, 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,z_3 are three complex numbers such that |z_1|=|z_2|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

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, 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, 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|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2()_, z_3 lie one a circle passing through e origin.

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

    Text Solution

    |

  2. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

    Text Solution

    |

  3. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

    Text Solution

    |

  4. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

    Text Solution

    |

  5. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

    Text Solution

    |

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

    Text Solution

    |

  7. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

    Text Solution

    |

  8. Find the range of (a) f(x) = (x^(2)+34 x - 71)/(x^(2) + 2x - 7) (b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find real value of theta for which (3+2i sin theta)/(1-2i sin theta) i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |