Home
Class 12
MATHS
If z1^2+z2^2+z3^2-z2z3-z3z4=0 Show that ...

If `z_1^2+z_2^2+z_3^2-z_2z_3-z_3z_4=0`
Show that
`|z_1-z_2|=|z_2-z_3|=|z_3-z_1|`

Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES (APPLICATION OF DEFINITE INTEGRALS)

    MBD PUBLICATION|Exercise QUESTION BANK|16 Videos

  • CONIC SECTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|179 Videos

Similar Questions

Explore conceptually related problems

If |z_1|le1,|z_2|le1"show that" |1-z_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2 "Hence or otherwise show that." |(z_1-z_2)/(1-z_1z_2)|lt 1"if"|z_1| lt 1,|z_2| lt 1

Show that Re(z_1z_2)=Rez_1Rez_2-Im z_1Imz_2 Im(z_1z_2)=Re z_1 Im z_2+Re z_2 Im z_1

If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz=1 when x,y,z are non zero and unequal.

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0

If x+y+z=xyz , prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) cdot(3y-y^3)/(1-3y^2)cdot(3z-z^3)/(1-3z^2)

MBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Solve the equationz^3=1+i

    Text Solution

    |

  2. Given cos alpha+cos beta +cos gamma=sin alpha+sin beta +sin gamma=0 S...

    Text Solution

    |

  3. If sin alpha + sin beta +sin gamma=0 =cos alpha+cos beta+cos gamma=0 "...

    Text Solution

    |

  4. If x+1/x=2cos theta,"Show that"x^n+1/x^n=2cos n theta

    Text Solution

    |

  5. xr=cos alphar+isinalphar. r=1,2,3 "and" x1+x2+x3=0 "Show that" 1/x1+1...

    Text Solution

    |

  6. Show that ((1+sintheta+icostheta)/(1+sintheta-icostheta))^n =cos((npi)...

    Text Solution

    |

  7. If alpha "and" beta "are roots "x^2-2x+4=0 "then show that"alpha^n+bet...

    Text Solution

    |

  8. For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((n...

    Text Solution

    |

  9. For a positive integer n show that (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) "...

    Text Solution

    |

  10. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

    Text Solution

    |

  11. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

    Text Solution

    |

  12. Solve x^9+x^5-x^4=1

    Text Solution

    |

  13. Find the general value of theta" if"(cos theta+isintheta)("cos"2theta+...

    Text Solution

    |

  14. If z=x+iy"show that" |x|+|y|lesqrt2|z|

    Text Solution

    |

  15. Show thatRe(z1z2)=Rez1Rez2-Im z1Imz2 Im(z1z2)=Re z1 Im z2+Re z2 Im z1

    Text Solution

    |

  16. What is the value of arg omega+ arg omega^2?

    Text Solution

    |

  17. If |z1|le1,|z2|le1"show that" |1-z1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2...

    Text Solution

    |

  18. If z1^2+z2^2+z3^2-z2z3-z3z4=0 Show that |z1-z2|=|z2-z3|=|z3-z1|

    Text Solution

    |

  19. Solve ((1-i)x+3i)/(2+i)+((3+2i)y+i)/(2-i)=-i "where" x, y, in R.

    Text Solution

    |

  20. Find the region on the Argand plane on which z satisfies1lt|z-2i|lt3

    Text Solution

    |