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If x-iy = sqrt((a+ib)/(c-id)), prove tha...

If `x-iy = sqrt((a+ib)/(c-id))`, prove that `(x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(2))`

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If x -iy = sqrt([(a - ib)/(c-id)]) , then (x^(2) + y^(2))^(2) =

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Knowledge Check

  • If sqrt([(a-ib)/(c-ib)])" then "(x^2+y^2)^2=

    A
    `((a^2+b^2))/((c^2-d^2))`
    B
    `((a^2-b^2))/((c^2+d^2))`
    C
    `((a^2+b^2))/((c^2+d^2))`
    D
    `((a^2-b^2))/((c^2-d^2))`

  • (d)/(dx ) {(sqrt(a^(2)+x ^(2))+ sqrt(a ^(2) -x ^(2)))/(sqrt(a ^(2) + x ^(2)) - sqrt(a ^(2) - x ^(2)))}=

    A
    `(2 a ^(2))/(x ^(2)){ 1+ (a ^(2))/(sqrt(a ^(4) -x ^(4)))}`
    B
    `(2 a ^(2))/(x ^(3)){ 1+ (a ^(2))/(sqrt(a ^(4) -x ^(4)))}`
    C
    `1+(a^(2))/( sqrt(a ^(4) -x ^(4)))`
    D
    `1- (a^(2))/( sqrt(a ^(4) -x ^(4)))`

  • If y = sqrt(cos 2x ) then y (d ^(2) y )/(dx ^(2)) + 2y ^(2) =

    A
    ` 0`
    B
    `- ((dx )/(dx))^(2)`
    C
    `((dy)/(dx)) ^(2)`
    D
    `y (dy)/(dx)`

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    If (x - iy) ^(1//3) = a - ib, then show that (x)/(a) + (y)/(b) = 4 ( a ^(2) - b ^(2)).

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    If cos x cos y=asin x+siny=b then prove that cos (x+y)=(a^(2)-b^(2))/(a^(2)+b^(2))

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