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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

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Since `(x+iy)^2=(a+ib)/(c+id)`
`rArr |x+iy|^2=(|a+ib|)/(|c+id|)" "[because|z_1/z_2|=|z_1|/(|z_2|)]`
`rArr (x^2+y^2)=sqrt(a^2+b^2)/(sqrt(c^2+d^2))`
`rArr (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)`
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