Home
Class 12
MATHS
If |z|<=1,|w|<=1, then show that |z- w|...

If ` |z|<=1,|w|<=1`, then show that `|z- w|^2<=(|z|-|w|)^2+(argz-argw)^2`

Text Solution

Verified by Experts

The correct Answer is:
`|z-w|^(2) le (|z|-|v|)^(2) ("arg z - arg w ")^(2)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

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_3|=......=|z_n|=1 , then |z_1+z_2+z_3+......+z_n|=

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=|z_2|=|z_3|=1 then value of |z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2 cannot exceed

If |z_1|=2, |z_2|=3, |z_3|=4 and |2z_1+3z_2 + 4z_3|=9 , then value of |8z_2z_3 + 27z_3z_1 + 64z_1z_2|^(1//3) is :

If |z_1|=1, |z_2|=2, |z_3|=3 and |9z_1z_2 + 4z_1z_3 + z_2z_3|=36 , then |z_1+z_2+z_3| is equal to _______.

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|=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-3|=min{|z-1|,|z-5|} , then Re(z) equals to

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

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

    Text Solution

    |

  2. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

    Text Solution

    |

  3. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

    Text Solution

    |

  4. Find the non-zero complex number z satisfying z =i z^2dot

    Text Solution

    |

  5. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

    Text Solution

    |

  6. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

    Text Solution

    |

  7. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

    Text Solution

    |

  10. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

    Text Solution

    |

  11. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

    Text Solution

    |

  12. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

    Text Solution

    |

  13. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

    Text Solution

    |

  14. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

    Text Solution

    |

  15. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

    Text Solution

    |

  16. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

    Text Solution

    |

  17. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

    Text Solution

    |

  18. Let z in c be such that |z| lt . If omega = (5 + 3z)/(5(1 - z)), then ...

    Text Solution

    |

  19. If z = ((1+i)^(2))/(alpha-i), alpha in R has magnitude sqrt((2)/(5)) ...

    Text Solution

    |

  20. Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=p...

    Text Solution

    |