Home
Class 12
MATHS
If x=cos alpha+i sin alpha,y=cos beta+is...

If `x=cos alpha+i sin alpha,y=cos beta+isinbeta,` then `(x-y)/(x+y)=`

A

`i.cos((alpha-beta)/(2))`

B

`i.sin((alpha-beta)/(2))`

C

`i.cot((alpha-beta)/(2))`

D

`i.tan((alpha-beta)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE -I|10 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x-y)/(x+y)

If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)-(y)/(x)

If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

If m, n integers and x = cos alpha + i sin alpha , y = cos beta + i sin beta, then prove that x^(m) y^(n) + 1/(x^(m)y^(n)) = 2 cos ( m alpha + n beta) " and " x^(m) y^(n) - 1/(x^(m) y^(n)) = 2 i sin ( m alpha + n beta) .

If x+1/x=2cos alpha,y+1/y=2cos beta, then xy+(1)/(xy)=

The real part of |(cos alpha+isin alpha, cos beta+ i sin beta),(sin beta+i cos beta, sin alpha +icos alpha)| is

If sin alpha = sin beta and cos alpha = cos beta then

The angle between the lines x cos alpha + y sin alpha=p_(1) and x cos beta+y sin beta=p_(2) where alpha gt beta is

AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

    Text Solution

    |

  2. If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)

    Text Solution

    |

  3. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then (x-y)/(x+y)=

    Text Solution

    |

  4. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

    Text Solution

    |

  5. If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)...

    Text Solution

    |

  6. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

    Text Solution

    |

  7. If n is positive integer and (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) cos...

    Text Solution

    |

  8. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)+beta^(n...

    Text Solution

    |

  9. Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i...

    Text Solution

    |

  10. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

    Text Solution

    |

  11. If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(...

    Text Solution

    |

  12. The values of (1-sqrt3i)^(1//3) are

    Text Solution

    |

  13. The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

    Text Solution

    |

  14. Two of the three values of (-1)^(1//3) are cos(pi//3)+isin(pi//3),cos(...

    Text Solution

    |

  15. One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

    Text Solution

    |

  16. If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z...

    Text Solution

    |

  17. If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multipl...

    Text Solution

    |

  18. If A+B+C=180^@ and cis A=x,cis B=y,cis C=z, them xyz=

    Text Solution

    |

  19. If xn=cos(pi/2^n)+isin(pi/2^n), then x1 x2 x3......infinity

    Text Solution

    |

  20. If zk=cos((kpi)/(10))+isin((kpi)/(10)) , then z1z2z3z4 is equal to

    Text Solution

    |