Home
Class 11
MATHS
Column I, Column II (Locus) parallelog...

Column I, Column II (Locus) parallelogram, p. `z_1-z_4=z_2-z_3` rectangle, q.`|z_1-z_(3|)=|z_2-z_(4|)` rhombus, r. `(z_1-z_2)/(z_3-z_4)` is purely real square, s.`(z_1-z_3)/(z_2-z_4)` is purely imaginary , t. `(z_1-z_2)/(z_3-z_2)` is purely imaginary

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 (5z_2)/(7z_1) is purely imaginary number then |(2z_1+3z_2)/(2z_1-3z_2) | is equal to

If (2z_(1))/(3z_(2)) is purely imaginary number, then |(z_(1)-z_(2))/(z_(1)+z_(2))|^(4) is equal to

If z_1, z_2 are complex number such that (2z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/(z_1+z_2)| .

If z_1, z_2 are complex number such that (2z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/(z_1+z_2)| .

Prove that |z_1+z_2|^2=|z_1|^2, ifz_1//z_2 is purely imaginary.

If z_1,z_2,z_3 are vertices of a triangle such that |z_1-z_2|=|z_1-z_3| then arg ((2z_1-z_2-z_3)/(z_3-z_2)) is :

If z_1,z_2,z_3 are vertices of a triangle such that |z_1-z_2|=|z_1-z_3| then arg ((2z_1-z_2-z_3)/(z_3-z_2)) is :

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

    Text Solution

    |

  2. The set of all possible real values of a such that the inequality (x-(...

    Text Solution

    |

  3. Column I, Column II (Locus) parallelogram, p. z1-z4=z2-z3 rectang...

    Text Solution

    |

  4. The interval of a for which the equation t a n^2x-(a-4)tanx+4-2a=0 has...

    Text Solution

    |

  5. The range of a for which the equation x^2+ax-4=0 has its smaller root ...

    Text Solution

    |

  6. Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 ...

    Text Solution

    |

  7. Consider the equation x^2+2x-n=0 where n in N and n in [5,100] The t...

    Text Solution

    |

  8. If n1, n2 are positive integers, then (1 + i)^(n1) + ( 1 + i^3)^(n1) +...

    Text Solution

    |

  9. The total number of values a so that x^2-x-a=0 has integral roots, wh...

    Text Solution

    |

  10. If i=sqrt-1, then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is e...

    Text Solution

    |

  11. Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and wi...

    Text Solution

    |

  12. If a r g(z)<0, then a r g(-z)-"a r g"(z) equals pi (b) -pi (d) -pi/2...

    Text Solution

    |

  13. Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniq...

    Text Solution

    |

  14. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

    Text Solution

    |

  15. if a lt c lt b, then check the nature of roots of the equation (a ...

    Text Solution

    |

  16. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

    Text Solution

    |

  17. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

  18. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

    Text Solution

    |

  19. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  20. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

    Text Solution

    |