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

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)`

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AI Generated Solution

To prove that \((x^2 + y^2)^2 = \frac{a^2 + b^2}{c^2 + d^2}\) given that \(x + iy = \sqrt{\frac{a + ib}{c + id}}\), we can follow these steps: ### Step 1: Start with the given equation We have: \[ x + iy = \sqrt{\frac{a + ib}{c + id}} \] ...
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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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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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