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If x+i y=sqrt((a+i b)/(c+i d)) prove tha...

If `x+i y=sqrt((a+i b)/(c+i d))` prove that `(x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)`

Text Solution

Verified by Experts

Given` x+iy = sqrt[(a+ib)/(c+id)]` ..(i)
`x-iy = sqrt[(a-ib)/(c-id)]` …(ii)
Multiply (i) and (ii)
`(x+iy)(x-iy) = sqrt[(a+ib)/(c+id)] sqrt[(a-ib)/(c-id)]`
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Knowledge Check

  • If x = iy = sqrt((a + i b)/( c + id)) , "then " (x^(2) + y^(2))^(2) is equal to

    A
    ` (a^(2) + b^(2))/(c^(2) + d^(2))`
    B
    `(c^(2) + d^(2))/(a^(2) + b^(2))`
    C
    `(a^(2) - b^(2))/(c^(2) - d^(2))`
    D
    none

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