Home
Class 11
MATHS
It is given that complex numbers z1 and ...

It is given that complex numbers `z_1` and `z_2` satisfy `|z_1|=2 `and `|z_2|=3.` If the included angled of their corresponding vectors is `60^0` , then find the value of `|(z_1+z_2)/(z_1-z_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

It is given the complex numbers z_(1) and z_(2) , |z_(1)| =2 and |z_(2)| =3 . If the included angle of their corresponding vectors is 60^(@) , then find value of |(z_(1) +z_(2))/(z_(1) -z_(2))|

Complex numbers z_(1) and z_(2) satisfy |z_(1)|=2 and |z_(2)|=3 . If the included angle of their corresponding vectors is 60^(@) , then the value of 19|(z_(1)-z_(2))/(z_(1)+z_(2))|^(2) is

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

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

For any two complex number z_1a n d\ z_2 prove that: |z_1+z_2|geq|z_1|-|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

    Text Solution

    |

  2. A certain polynomial P(x), x in R when divided by x-a ,x-b and x-c le...

    Text Solution

    |

  3. It is given that complex numbers z1 and z2 satisfy |z1|=2 and |z2|=3....

    Text Solution

    |

  4. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

    Text Solution

    |

  5. If theta is real and z1, z2 are connected by z1 2+z2 2+2z1z2costheta=0...

    Text Solution

    |

  6. If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the val...

    Text Solution

    |

  7. Show that a real value of x will satisfy the equation (1-i x)//(1+i x)...

    Text Solution

    |

  8. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

    Text Solution

    |

  9. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

    Text Solution

    |

  10. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

    Text Solution

    |

  11. Solve :z^2+|z|=0 .

    Text Solution

    |

  12. If roots of equation x^2-2c x+a b=0 are real and unequal, then prove ...

    Text Solution

    |

  13. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |

  14. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

    Text Solution

    |

  15. If (1+i)^2 /(3 - i) , then Re(z) =

    Text Solution

    |

  16. Find the quadratic equation with rational coefficients whose one root ...

    Text Solution

    |

  17. Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then...

    Text Solution

    |

  18. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac!=0, then prove that f...

    Text Solution

    |

  19. Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of ...

    Text Solution

    |

  20. If x is real, then x//(x^2-5x+9) lies between -1a n d-1//11 b. 1a n d-...

    Text Solution

    |