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If (1-ix)/(1+ix)=a-ibanda^(2)+b^(2)=1,wh...

If `(1-ix)/(1+ix)=a-ibanda^(2)+b^(2)=1,where` `a,b in Randi=sqrt(-1),` then xis equal to

A

`(2a)/((1+a)^(2)+b^(2))`

B

`(2b)/((1+a)^(2)+b^(2))`

C

`(2a)/((1+b)^(2)+a^(2))`

D

`(2b)/((1+b)^(2)+a^(2))`

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Show that a real value of x will satisfy the equation (1-ix)/(1+ix)=a-ibquad if a^(2)+b^(2)=1 ,when a,b are real.

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Knowledge Check

  • If a^(2) + b^(2) = 1 then (1 + a + ib)/( 1 + a - i b) is equal to

    A
    a+ib
    B
    a-ib
    C
    b+ia
    D
    b-ia

  • If A={1,B} ,where B = {2,3} .Then, P(A) is equal to

    A
    `{{1}, {B}, {1, B}}`
    B
    `{ phi, { 1} , { B } , { 1, B } }`
    C
    `{ phi, { 1 } , { B } }`
    D
    None of these

  • If x^(2) + y^(2) = 1 and x ne -1 then (1+y+ix)/(1+y-ix) equals

    A
    1
    B
    x + iy
    C
    2
    D
    y + ix

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