Home
Class 12
MATHS
If z(1)^(2)+z(2)^(2)+z(3)^(2)-z(1)z(3)-z...

If `z_(1)^(2)+z_(2)^(2)+z_(3)^(2)-z_(1)z_(3)-z_(1)z_(2)-z_(2)z_(3)=0" ""prove that" " "|z_(2)-z_(3)|=|z_(3)-z_(1)|=|z_(1)-z_(2)|, "where" " " z_(1),z_(2),z_(3)` are complex numbers.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVEEXAMS(Multiple Corrrect Answer type)|7 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise EXERCISE 4(SHORT ANSWER TYPE QUESTION )|58 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (E. Assertion-Reason Type)|2 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

If z_(1)=4-3iand z_(2)=-12+5i, "show that", |z_(1)z_(2)|=|z_(1)||z_(2)|

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |z_(1)z_(2)|=|z_(1)||z_(2)|

If |z_(1)|=|z_(2)|and argz_(1)~argz_(2)=pi, "show that" " " z_(1)+z_(2)=0.

If z_(1)=4-3iand z_(2)=-12+5i, "show that", |z_(1)/z_(2)|=|z_(1)|/|z_(2)|

If amp(z_(1)z_(2))=0and |z_(1)|=|z_(2)|=1, "then"

If z_(1)=4-3iand z_(2)=-12+5i, "show that", |z_(1)+z_(2)|lt|z_(1)|+|z_(2)|

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |z_(1)+z_(2)|lt|z_(1)|+|z_(2)|

If |z_(1)|=|z_(2)|and argz_(1)+argz_(2)=0, then show that z_(1) and z_(2) are tow complex conjugate numbers. '

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)

CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
  1. If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))...

    Text Solution

    |

  2. If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-...

    Text Solution

    |

  3. If y=sqrt(x^(2)+6x+8), show that one value of sqrt(1+iy)+sqrt(1-iy)[i...

    Text Solution

    |

  4. Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

    Text Solution

    |

  5. prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc...

    Text Solution

    |

  6. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  7. Express each of the following expressions as the sum of two squares: ...

    Text Solution

    |

  8. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  9. If a,b are real and a^(2)+b^(2)=1 then show that the equation (sqrt(1...

    Text Solution

    |

  10. If z=x+iy and |z|=1, show that (z-1)/(z+1)(z!=-1) is a purely imaginar...

    Text Solution

    |

  11. If z(1)and z(2) be any two non-zero complex numbers such that |z(1)+z(...

    Text Solution

    |

  12. If alpha be the real positive cube root and beta,gamma be the complex ...

    Text Solution

    |

  13. If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex ...

    Text Solution

    |

  14. In the complex plane, the vertices of an equlitateral triangle are rep...

    Text Solution

    |

  15. Show that the area of the triangle on the Argrand Diagram formed by th...

    Text Solution

    |

  16. If z(1)^(2)+z(2)^(2)+z(3)^(2)-z(1)z(3)-z(1)z(2)-z(2)z(3)=0" ""prove th...

    Text Solution

    |

  17. Solve bar(z)=iz^(2) (z being a complex number)

    Text Solution

    |

  18. Solve : |z|+z=2+i (z being a complex number)

    Text Solution

    |

  19. If z=x+iy then show that |x|+|y|lesqrt2|x+iy|.

    Text Solution

    |

  20. Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the comple...

    Text Solution

    |