Home
Class 11
MATHS
If |z1-z0|=|z2-z0|=a and amp((z2-z0)/(z0...

If `|z_1-z_0|=|z_2-z_0|=a` and `amp((z_2-z_0)/(z_0-z_1))=pi/2` , then find `z_0`

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=2-i, z_2=1+i, find abs((z_1+z_2+1)/(z_1-z_2+i))

if amp (z-1)/(z+1)=pi/3 , then the locus of z is

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot

If z_(1) , z_(2) are complex numbers such that Re(z_(1))=|z_(1)-2| , Re(z_(2))=|z_(2)-2| and arg(z_(1)-z_(2))=pi//3 , then Im(z_(1)+z_(2))=

If amp (z_1z_2)=0 and absz_1=absz_2=1 , then

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 find |z_(1)+z_(2)+z_(3)| .

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

If |z_1|=|z_2|=|z_3|=1 and z_1+z_2+z_3=0 then the area of the triangle whose vertices are z_1, z_2, z_3 is 3sqrt(3)//4 b. sqrt(3)//4 c. 1 d. 2

If |z_(1)|=|z_(2)|=1 and argz_(1)+argz_(2)=0 then show that z_(1)=1

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

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Roots of the equation are (z+1)^5=(z-1)^5 are (a) +-itan(pi/5),+-ita...

    Text Solution

    |

  2. Find the value of a for which one root of the quadratic equation (a^2-...

    Text Solution

    |

  3. If |z1-z0|=|z2-z0|=a and amp((z2-z0)/(z0-z1))=pi/2 , then find z0

    Text Solution

    |

  4. Which of the following represents a points in an Argand pane, equidi...

    Text Solution

    |

  5. If the harmonic mean between roots of (5+sqrt(2))x^2-b x+8+2sqrt(5)=0i...

    Text Solution

    |

  6. If n in N >1 , then the sum of real part of roots of z^n=(z+1)^n is...

    Text Solution

    |

  7. If z1, z2, z3, z4 are the affixes of four point in the Argand plane, z...

    Text Solution

    |

  8. Find the values of the parameter a such that the rots alpha,beta of ...

    Text Solution

    |

  9. Solve the equation z^3= z (z!=0)dot

    Text Solution

    |

  10. If z=omega,omega^2 where omega is a non-real complex cube root of unit...

    Text Solution

    |

  11. Let alphaa n dbeta be the solutions of the quadratic equation x ^2-11...

    Text Solution

    |

  12. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

    Text Solution

    |

  13. If 1,Z1,Z2,Z3,........Z(n-1) are n^(th) roots of unity then the value...

    Text Solution

    |

  14. If a ,b ,c in R^+and 2b=a+c , then check the nature of roots of equat...

    Text Solution

    |

  15. If z is a complex number such taht z^2=( barz)^2, then find the loc...

    Text Solution

    |

  16. If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies ...

    Text Solution

    |

  17. Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3...

    Text Solution

    |

  18. Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

    Text Solution

    |

  19. P(z1),Q(z2),R(z3)a n dS(z4) are four complex numbers representing the ...

    Text Solution

    |

  20. Given that the expression 2x^3+3p x^2-4x+p has a remainder of 5 when d...

    Text Solution

    |