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(i) If x+iy=(a+ib)/(a-ib), prove that x^...

(i) If `x+iy=(a+ib)/(a-ib)`, prove that `x^(2)+y^(2)=1`.
(ii) If `((a+i)^(2))/(2a-i)=p+iq`, prove that:
`p^(2)+q^(2)=((a^(2)+1)^(2))/(4a^(2)+1)`.

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