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If a+i b=((x+i)^2)/(2x+1) , prove that a...

If `a+i b=((x+i)^2)/(2x+1)` , prove that `a^2+b^2=((x+i)^2)/((2x+1)^2)`

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`a+ ib = ((x+i)^(2))/(2x^(2) + 1)`
`or |a+ib| = |((x+i)^(2))/(2x^(2)+1)|`
`or sqrt(a^(2) + b^(2))=(|x+i|)/(2x^(2) +1)`
`or a^(2) + b^(2) = ((x^(2)+1)^(2))/((2x^(2) + 1)^(2))`
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