If `x + i y =(a+i b)/(a-i b),`prove that `x^2+y^2=1`. – InterviewSolution

InterviewSolution

1.	If `x + i y =(a+i b)/(a-i b),`prove that `x^2+y^2=1`.
Answer» `(x+iy)=(a+ib)/(a-ib) rArr bar((x+iy))=((bar(a+ib)))/((bar(a-ib))) rArr (x-iy) = ((a-ib))/((a+ib))`. `therefore" "(x+iy)(x-iy)=((a+ib))/((a-ib))xx((a-ib))/((a+ib))=1 rArr x^(2) + y^(2) = 1`.

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