Home
Class 11
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

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|=|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).

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the non-zero complex number z satisfying z =i z^2dot

    Text Solution

    |

  2. Let a,b and c be real numbers such that 4a+2b+c=0 and ab gt 0.Then t...

    Text Solution

    |

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

    Text Solution

    |

  4. If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equa...

    Text Solution

    |

  5. For complex numbers z and w, prove that |z|^2w- |w|^2 z = z - w, if...

    Text Solution

    |

  6. If alpha,beta are the roots of the equation a x^2+b x+c=0, then the va...

    Text Solution

    |

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

    Text Solution

    |

  8. If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt...

    Text Solution

    |

  9. The maximum value of |a r g(1/(1-z))| for |z|=1,z!=1 is given by.

    Text Solution

    |

  10. If one root is square of the other root of the equation x^2+p x+q=0, t...

    Text Solution

    |

  11. If z^4+1=sqrt(3)i (A) z^3 is purely real (B) z represents the vertic...

    Text Solution

    |

  12. Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 an...

    Text Solution

    |

  13. If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i, where...

    Text Solution

    |

  14. Let alpha,beta be the roots of x^2-x+p=0a n dgamma,delta are roots of ...

    Text Solution

    |

  15. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  16. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  17. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  18. For the equation 3x^2+p x+3=0,p >0, if one of the root is square of th...

    Text Solution

    |

  19. Let z,w be complex numbers such that barz+ibarw=0 and arg zw=pi Then a...

    Text Solution

    |

  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) be the minimum value of f(x)do...

    Text Solution

    |