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If (x - iy) ^(1//3) = a - ib, then show ...

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

Text Solution

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The correct Answer is:
`4 (a^2 - b^2)`
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Knowledge Check

  • If (x-iy ) ^(1/3) = a + ib, then (ax -by)/(a-b) =

    A
    `a ^(3) -b ^(3)`
    B
    `a ^(3) + a ^(2) b+ab ^(2) + b ^(3)`
    C
    ` a ^(3) + 3a ^(2) b+ 3ab^(2) + b ^(2)`
    D
    `a ^(4) -b ^(4)`

  • If (x + iy)^((1)/(3)) = a+ ib , then ((x)/(a)) + ((y)/(b)) =

    A
    `a^(2) - b^(2)`
    B
    `4 (a^(2) - b^(2))`
    C
    `2(a^(2) - b^(2))`
    D
    `2 (a ^(2) + b^(2))`

  • If cos ( x+ iy) = A + iB, then A =

    A
    cos x cosh y
    B
    sin x sinh y
    C
    `-sin x sinh y `
    D
    `cos x sinh y `

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