Home
Class 12
MATHS
Let z(1)" and "z(2) be two complex numbe...

Let `z_(1)" and "z_(2)` be two complex numbers such that `z_(1)z_(2)" and "z_(1)+z_(2)` are real then

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED|59 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.1|6 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

If z_(1)" and "z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 then

If z_(1)" and "z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0, Im(z_(1)z_(2))=0 then

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg z_(1)- arg z_(2) is equal to

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg ((z_1)/(z_2)) is equal to

Let z_(1)" and "z_(2) be complex numbers such that z_(1)+ i(bar(z_2))=0" and "arg(bar(z_1)z_2)=(pi)/(3) . Then arg(bar(z_1)) is

a. Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=rgt0 and z_(1)+z_(2)+z_(3)!=0 . Prove that |(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))/(z_(1)+z_(2)+z_(3))|=r b. Find all cube roots of sqrt(3)+i .

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

FULL MARKS-COMPLEX NUMBERS -EXERCISE - 2.9
  1. Let z(1)" and "z(2) be two complex numbers such that z(1)z(2)" and "z(...

    Text Solution

    |

  2. i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)

    Text Solution

    |

  3. The value of sum(i=1)^(13) (n^(n) + i^(n-1)) is

    Text Solution

    |

  4. The area of the triangle formed by the complex numbers z, iz, and z + ...

    Text Solution

    |

  5. The conjugate of a complex number is (1)/(i-2). Then, the complex numb...

    Text Solution

    |

  6. If z= ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)), then |z| is equal...

    Text Solution

    |

  7. If z is non zero complex number, such that 2i z^(2) = bar(z),then |z| ...

    Text Solution

    |

  8. If |z-2 + i|le2, then the greatest value of |z| is

    Text Solution

    |

  9. If |z - (3)/(z)| = 2, then the least value of |z| is

    Text Solution

    |

  10. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

    Text Solution

    |

  11. The solution of the equation |z| -z = 1 + 2i is

    Text Solution

    |

  12. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

    Text Solution

    |

  13. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

    Text Solution

    |

  14. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

    Text Solution

    |

  15. If (z - 1)/(z + 1) is purely imaginary, then |z| is

    Text Solution

    |

  16. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

    Text Solution

    |

  17. The principal argument of (3)/(-1 + i) is

    Text Solution

    |

  18. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

    Text Solution

    |

  19. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

    Text Solution

    |

  20. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

    Text Solution

    |

  21. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

    Text Solution

    |