Home
Class 11
MATHS
If alpha and beta are different complex...

If `alpha and beta` are different complex number with `|beta|=1`, then find `|(beta-alpha)/(1-bar alpha beta)|`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`|(beta-alpha)/(1-bar(alpha)beta)|^(2)=(( beta-alpha)/(1-bar(alpha)beta)) *bar(((beta-alpha)/(1-baralphabeta)))`
`=((beta-alpha)(bar(beta)-baralpha))/(( 1- bar alphabeta)(1-alphabarbeta))=(betabarbeta+alphabaralpha-alphabarbeta-baralpha beta )/(1+ alphabaralphabetabarbeta-alphabarbeta-baralphabeta)`
`" "=(|beta|^(2) + |alpha|^(2)-alphabarbeta-baralphabeta)/(1+|alpha|^(2)|beta|^(2)-alphabarbeta-baralphabeta)`
` " "=(1+|alpha|^(2)-alphabarbeta-baralphabeta)/(1+|alpha|^(2) -alphabarbeta-bar alphabeta)=1`
`rArr" "|(beta-alpha)/(1-baralphabeta)|=1`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5.3|10 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Example|68 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are different complex numbers with |beta|=1, then find |(beta-alpha)/(1- baralphabeta)| .

If alpha and beta Are different complex number with |alpha|=1, then what is |(alpha- beta)/(1-alpha beta)| equal to ?

If alpha,beta are different complex numbers with | beta|=1 then |(alpha-beta)/(1-alphabar(beta))|=(i)0(ii)(1)/(2)(iii)1(iv)2

If alpha and beta are the complex cube roots of unity, then what is the vlaue of (1+alpha)(1+beta)(1+alpha^(2))(1+beta^(2)) ?

NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
  1. Evaluate : [i^(18)+(1/i)^(25)]^3

    Text Solution

    |

  2. Prove that Re (z1 z2)= Re z1 Re z2 - Imz1 Imz2 ,

    Text Solution

    |

  3. Reduce (1/(1-4i)-2/(1+i))((3-4i)/(5+i))to the standard form.

    Text Solution

    |

  4. If (a+i b)/(c+i d)=x+i y , prove that (a-i b)/(c-i d)=x-i ya n d(a^2+b...

    Text Solution

    |

  5. Convert the following in the polar form : (i) (1+7i)/((2-i)^2) (ii) (...

    Text Solution

    |

  6. Solve the equation : 3x^2-4x+(20)/3=0

    Text Solution

    |

  7. x^(2)-2x+(3)/(2)=0

    Text Solution

    |

  8. Solve the equation :27 x^2-10 x+1=0

    Text Solution

    |

  9. Solve the following quadratic: 21 x^2-28 x+10=0

    Text Solution

    |

  10. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

    Text Solution

    |

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

    Text Solution

    |

  12. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 bar...

    Text Solution

    |

  13. Find the modulus and argument of the complex number (1+2i)/(1-3i).

    Text Solution

    |

  14. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

    Text Solution

    |

  15. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i).

    Text Solution

    |

  16. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

    Text Solution

    |

  17. If alpha and beta are different complex number with |beta|=1, then f...

    Text Solution

    |

  18. Find the number of non-zero integral solutions of the equation |1-i|^...

    Text Solution

    |

  19. If (a + i b) (c + i d) (e + i f) (g + i h) = A + i B, then show that (...

    Text Solution

    |

  20. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

    Text Solution

    |