Home
Class 11
MATHS
z1a n dz2 lie on a circle with center at...

`z_1a n dz_2` lie on a circle with center at the origin. The point of intersection `z_3` of he tangents at `z_1a n dz_2` is given by `1/2(z_1+( z )_2)` b. `(2z_1z_2)/(z_1+z_2)` c. `1/2(1/(z_1)+1/(z_2))` d. `(z_1+z_2)/(( z )_1( z )_2)`

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 |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

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

If z_1nez_2 and abs(z_2)=1 the abs((z_1-z_2)/(1-barz_1z_2)) =

For any two complex numbers z_1 and z_2 , , prove that Re (z_1 z_2) = Re z_1 Re z_2 – Imz_1 Imz_2

if z_1=1+isqrt3 , z_2=sqrt3-i show that (a)arg (z_1z_2)=arg(z_1)+arg(z_2) and (b) arg(z_1//z_2)=arg(z_1)-arg(z_2)

If the tangents at z_(1) , z_(2) on the circle |z-z_(0)|=r intersect at z_(3) , then ((z_(3)-z_(1))(z_(0)-z_(2)))/((z_(0)-z_(1))(z_(3)-z_(2))) equals

Let z_1 and z_2 are two complex nos s.t. abs(z_1) =abs(z_2)=1 then abs((z_1-z_2)/(1-z_1 barz_2)) is equal to

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

Let vertices of an acute-angled triangle are A(z_1),B(z_2),a n dC(z_3)dot If the origin O is the orthocentre of the triangle, then prove that z_1 bar z _2+ bar z _1z_2=z_2 bar z _3+ bar z _2z_3=z_3 bar z _1+ bar z _3z_1

An equilateral triangle in the Argan plane has vertix as z_1 , z_2 and z_3 which are there complex no show that 1/(z_1-z_2)+1/(z_3-z_1)+1/(z_2-z_3)=0

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  2. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |

  3. z1a n dz2 lie on a circle with center at the origin. The point of inte...

    Text Solution

    |

  4. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

    Text Solution

    |

  5. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

    Text Solution

    |

  6. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

    Text Solution

    |

  7. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

    Text Solution

    |

  8. Find a quadratic equation whose product of roots x1 and x2 is equa...

    Text Solution

    |

  9. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

    Text Solution

    |

  10. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

    Text Solution

    |

  11. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

    Text Solution

    |

  12. Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C ...

    Text Solution

    |

  13. Convert (1+3i)/(1-2i) into the polar form.

    Text Solution

    |

  14. If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is ...

    Text Solution

    |

  15. Let the altitudes from the vertices A, B and C of the triangle ABC me...

    Text Solution

    |

  16. For |z-1|=1, show that tan{[a r g(z-1)]/2}-((2i)/z)=-i

    Text Solution

    |

  17. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  18. If z1=9y^2-4-10ix,z2=8y^2-20i where z1=barz2 then z=x+iy is equal to

    Text Solution

    |

  19. If a rg(z1)=170^0 and arg(z2)=70^0 , then find the principal argument...

    Text Solution

    |

  20. z1, z2 and z3 are the vertices of an isosceles triangle in anticlockwi...

    Text Solution

    |