Home
Class 11
MATHS
z(1) and z(2) are two complex number suc...

`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)`

Text Solution

Verified by Experts

The correct Answer is:
`:. z_(1)=-barz_(2) " " [ :. barz_(2)=r_(2)(cos theta_(2)- sin theta_(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

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

State true of false for the following: Let z_(1) and z_(2) be two complex number's such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg (z_(1)-z_(2))=0

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 arg (z_(1))-arg(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear.

If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)=(pi)/(2) then show that barzw=-i

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)| .

If z_1 and z_2 , are two non-zero complex numbers such tha |z_1+z_2|=|z_1|+|z_2| then arg(z_1)-arg(z_2) is equal to

IF (1+i)z=(1-i)z, then show that z=-barz .

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.

A complex number z is said to be unimodular if abs(z)=1 . Suppose z_(1) and z_(2) are complex numbers such that (z_(1)-2z_(2))/(2-z_(1) bar z_(2)) is unimodular and z_(2) is not unimodular. Then the point z_(1) lies on a

If |z_(1)|=|z_(2)| , is the necessary that z_(1)=z_(2)

KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)
  1. Show that |(z-2)/(z-3)|=2 represents a circle. Find the centre of radi...

    Text Solution

    |

  2. If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value ...

    Text Solution

    |

  3. z(1) and z(2) are two complex number such that |z(1)|=|z(2)| and arg (...

    Text Solution

    |

  4. If |z(1)|=1(z(1) ne -1) and z(2)=(z(1)-1)/(z(1)+1) then show that the ...

    Text Solution

    |

  5. If z(1), z(2) and z(3), z(4) are two pairs of conjugate complex number...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |