Home
Class 12
MATHS
For complex numbersz1=x1+iy1" and " z2=x...

For complex numbers`z_1=x_1+iy_1" and " z_2=x_2+iy_2` we write `z_1 cap z_2` if `x_1 le X_2 and y_1 le y_2` Then for all compelx nubers z with `1 cap z` we have `(1-z)/(1+z) cap 0 `

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

For complex numbers z_(1)=x_(1)+iy_(1) and z_(2)=x_(2)+iy_(2), (where i=sqrt(-1) ) we write z_(1)nn z_(2) of x_(1)<=x_(2) and y_(1)<=y_(2), then for all complex number z with 1nn z, we have (1-z)/(1+z)nn... is

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If z_1 , z_2 are nonreal complex and |(z_1+z_2)/(z_1-z_2)| =1 then (z_1)/(z_2) is

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1, then

If z_1,z_2 are nonzero complex numbers then |(z_1)/(|z_1|)+(z_2)/(|z_2|)|le2 .

For any complex number z=x+ iy,define (z)=|x|+|y|. If z_(1) and z_(2) are any two complex numbers,then (1) (z_(1)+z_(2))lt=(z_(1))+(z_(2)) (2) (z_(1)+z_(2))=(z_(1))+(z_(2)) (3) (z_(1)+z_(2))gt=(z_(1))+(z_(2)) (4) (z_(2)-z_(1))=(z_(2))-(z_(1))

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta)...

    Text Solution

    |

  2. If two nonzero complex numbers z1,z2 be such that z1+z2 is real then t...

    Text Solution

    |

  3. For complex numbersz1=x1+iy1" and " z2=x2+iy2 we write z1 cap z2 if x1...

    Text Solution

    |

  4. If z is a nonzero complex number then (bar(z^-1))=(barz)^-1 .

    Text Solution

    |

  5. If the points P and Q represent the complex numbers z and iz then angl...

    Text Solution

    |

  6. If z1ne-z2 and |z1+z2|=|1/z1 + 1/z2| then :

    Text Solution

    |

  7. Find z, if |(z+1)/(z+i)|=1

    Text Solution

    |

  8. If in the Argand plane z1,z2,z3 and z4 are four points such that |z1|=...

    Text Solution

    |

  9. State true or false: If zne0 then argz+argbarz=0.

    Text Solution

    |

  10. Let z1 and z2 be the roots of z^2+pz+q=0. Then the points represented ...

    Text Solution

    |

  11. If z1,z2 are nonzero complex numbers then |(z1)/(|z1|)+(z2)/(|z2|)|le2...

    Text Solution

    |

  12. The nth roots of -1 can be n terms of a GP.

    Text Solution

    |

  13. In the following, each question has one or more than one correct answe...

    Text Solution

    |

  14. If |z-3i|=3 and amp z in (0, pi/2), then cot(amp z)-theta/z is eqaul ...

    Text Solution

    |

  15. If zne0 then amp z +ampbarz = .

    Text Solution

    |

  16. x+iy=((sqrt3+i)/(1-sqrt3i))^25 then x=, y=.

    Text Solution

    |

  17. If alpha1,alpha2,alpha3,alpha4 be the roots of x^5-1=0 then prove that...

    Text Solution

    |

  18. Consider the quadratic equation az^(2)+bz+c=0 where a,b,c and non-zero...

    Text Solution

    |

  19. If |z^2-4|=2|z| then find the greatest value of |z|.

    Text Solution

    |

  20. If z=2 + t + i sqrt(3-t^2), where t is real and t^2 lt 3, show that t...

    Text Solution

    |