Home
Class 12
MATHS
If |z-1| <3, prove that |iz+3-5i| < 8....

If `|z-1| <3`, prove that `|iz+3-5i| < 8`.

Text Solution

AI Generated Solution

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

If |z_1-1|=Re(z_1),|z_2-1|=Re(z_2) and arg (z_1-z_2)=pi/3, then Im (z_1+z_2) =

If |z_(1)|=|z_(2)|=......=|z_(n)|=1, prove that |z_(1)+z_(2)+z_(3)++z_(n)|=(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))++(1)/(z_(n))

If |z_(1)|=|z_(2)|=...............=|z_(n)|=1 then |(1)/(z_(1))+(1)/(z_(2))+.........+(1)/(z_(n))|

If |z_(1)| = |z_(2)| = 1, z_(1)z_(2) ne -1 and z = (z_(1) + z_(2))/(1+z_(1)z_(2)) then

If |z_(1)|!=1,|(z_(1)-z_(2))/(1-bar(z)_(1)z_(2))|=1, then

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If |z|=1 and z ne +-1 , then one of the possible value of arg(z)-arg(z+1)-arg(z-1) , is

If |z|=1 and z'=(1+z^(2))/(z) , then

If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then Re(w) is 0(b)(1)/(|z+1|^(2))|(1)/(z+1)|,(1)/(|z+1|^(2))(d)(sqrt(2))/(|z|1|^(2))

If |z| = 1 , then ((1 + z)/(1 + z)) equals :

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

    Text Solution

    |

  2. Prove that |1-barz1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2).

    Text Solution

    |

  3. If |z-1| <3, prove that |iz+3-5i| < 8.

    Text Solution

    |

  4. Prove that for nonzero complex numbers |z1+z2| |frac(z1)(|z1|)+frac(z2...

    Text Solution

    |

  5. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

    Text Solution

    |

  6. Find the value of w^4+w^6+w^8, if w is a complex cube root of unity.

    Text Solution

    |

  7. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |

  8. If a, b are real, prove that the equation z^2+az+b=0 will not have any...

    Text Solution

    |

  9. Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

    Text Solution

    |

  10. If |z|ge3, then determine the least value of |z+(1)/(z)|.

    Text Solution

    |

  11. If z is a complex number such that |z+1/z|=1 show that Re(z)=0 when |z...

    Text Solution

    |

  12. Locate the region in the Argand plane for the complex number z satisfy...

    Text Solution

    |

  13. Indicate the region represented by pi/6leargzlepi/4 .

    Text Solution

    |

  14. Indicate the region in the Argand plane respresented by |z+1|^2+|z-1|^...

    Text Solution

    |

  15. Prove that the product of any number of unimodular complex numbers is ...

    Text Solution

    |

  16. Separate the real and imaginary parts of frac((cosalpha+isinalpha)(cos...

    Text Solution

    |

  17. Prove that (frac(1+costheta+isintheta)(1+costheta-isintheta))^n=cos nt...

    Text Solution

    |

  18. If alpha=pi/12 ,prove that frac((cosalpha+isinalpha)(cos2alpha+isin2al...

    Text Solution

    |

  19. Prove that (frac(cosx+isinx)(sinx+icosx))^5=cos(10x-frac(5pi)(2))+isin...

    Text Solution

    |

  20. Find the value of : root(4)(1).

    Text Solution

    |