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)`

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

If z_1=2-i ,\ z_2=1+i , find |(z_1+z_2+1)/(z_1-z_2+i)| .

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

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

If |z_1|=1a n d|z_2|=2,t h e n Max (|2z_1-1+z_2|)=4 Min (|z_1-z_2|)=1 |z_2+1/(z_1)|lt=3 Min (|z_1=z_2|)=2

Which of the following is correct for any tow complex numbers z_1a n dz_2? (a) |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

Which of the following is correct for any tow complex numbers z_1a n dz_2? |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

If z_1ne-z_2 and |z_1+z_2|=|1/z_1 + 1/z_2| then :

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2

For two complex numbers z_1&z_2 (a z_1+b z_1)(c z_2+d z_2)=(c z_1+bz_2)if(a , b , c , d in R):

CENGAGE ENGLISH-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 Cof the triangle e ABCmee...

    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=overline z2, then find z=x+i...

    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

    |