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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)`

Answer» We have
`(x+iy)=sqrt((a+ib)/(c+id))=(sqrt(a+ib))/(sqrt(c+id))`
`rArr" "(x-iy)=(sqrt(a-ib))/(sqrt(c-id))`
`rArr" "(x+iy)(x-iy)=(sqrt(a+ib))/(sqrt(c+id))xx(sqrt(a-ib))/(sqrt(c-id))=(sqrt((a+ib)(a-ib)))/(sqrt((c+id)(c-id)))`
`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)))`.
Hence, `(x^(2)+y^(2))^(2)=((a^(2)+b^(2)))/((c^(2)+d^(2)))`.


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