Home
Class 11
MATHS
If the complex numbers z(1) and z(2) arg...

If the complex numbers `z_(1) and z_(2) arg (z_(1))- arg(z_(2))=0` then showt aht `|z_(1)-z_(2)|=|z_(1)|-|z_(2)|`.

Text Solution

Verified by Experts

The correct Answer is:
`=|z_(1)|-|z_(2)|`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (Match Column & Short Questions)|15 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (Objective type questions)|16 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|11 Videos

  • BINOMIAL THEOREM

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|7 Videos

  • CONIC SECTIONS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|9 Videos

Similar Questions

Explore conceptually related problems

z_(1) and z_(2) are two complex number such that |z_(1)|=|z_(2)| and arg (z_(1))+arg(z_(2))=pi , then show that z_(1)=-barz_(2)

If |z_(1)|=|z_(2)|andamp(z_(1))+amp(z_(2))=0, then

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(1)/(z))=2 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(2)/(z))=4 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(3)/(z))=6 and sum of greatest and least values of abs(z) is 2lambda , then lambda^(2) , is

|z_(1)+z_(2)|=|z_(1)|+|z_(2)| is possible, if

z_(1)=9+3i and z_(2)=-2-i then find z_(1)-z_(2)

Let z_(1)z_(2)andz_(3) be three complex numbers and a,b,cin R, such that a+b+c=0andaz_(1)+bz_(2)+cz_(3)=0 then show that z_(1)z_(2)and z_(3) are collinear.

If iz^(3)+z^(2)-z+i=0 then show that |z|=1.

KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)
  1. If z(1), z(2) and z(3), z(4) are two pairs of conjugate complex number...

    Text Solution

    |

  2. If |z(1)|=|z(2)|=....|z(n)|=1, then show that, |z(1)+z(2)+z(3)+....z(n...

    Text Solution

    |

  3. If the complex numbers z(1) and z(2) arg (z(1))- arg(z(2))=0 then show...

    Text Solution

    |

  4. Solve the system of equation Re(z^(2))=0,|z|=2.

    Text Solution

    |

  5. Find the complex number satsifying the equation z+sqrt(2)|(z+1)|+i=0

    Text Solution

    |

  6. Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the pola...

    Text Solution

    |

  7. If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)...

    Text Solution

    |

  8. Fill in the blanks of the following For any two complex numbers z(1)...

    Text Solution

    |

  9. Fill in the blanks of the following the value of sqrt(-25)xxsqrt(-9)...

    Text Solution

    |

  10. Fill in the blanks of the following The number ((1-i)^(2))/(1-i^(3))...

    Text Solution

    |

  11. Fill in the blanks of the following The sum of the series i+i^(2)+i^...

    Text Solution

    |

  12. Fill in the blanks of the following Multiplicative inverser of 1+I i...

    Text Solution

    |

  13. Fill in the blanks of the following If z(1) and z(2) are complex num...

    Text Solution

    |

  14. Fill in the blanks of the following arg(z)+ arg(barz) where (barz ne...

    Text Solution

    |

  15. Fill in the blanks of the following If |z+4| le3, then the greatest ...

    Text Solution

    |

  16. Fill in the blanks of the following If |(z-2)/(z+2)|=(pi)/(6) then t...

    Text Solution

    |

  17. Fill in the blanks of the following If |z|=4" and arg"(z)=(5pi)/(6),...

    Text Solution

    |

  18. State true of false for the following: The order relation is defined...

    Text Solution

    |

  19. State true of false for the following: Multiplication of a non-zero ...

    Text Solution

    |

  20. State true of false for the following: For any complex number, z, th...

    Text Solution

    |