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If x+iy=(a+ib)/(a-ib) prove that x^2+y^...

If ` x+iy=(a+ib)/(a-ib)` prove that `x^2+y^2=1`

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Given, `x+iy=(a+ib)/(a-ib)=((a+ib)(a+ib))/((a-ib)(a+ib))=(a^2-b^2+i2ab)/(a^2+b^2)`
`impliesx=(a^2-b^2)/(a^2+b^2)and y=(2ab)/(a^2+b^2)
Then, `x^2+y^2=((a^2-b^2)/(a^2+b^2))^2+((2ab)/(a^2+b^2))^2=((a^2-b^2)^2+(2ab)^2)/((a^2+b^2)^2)=(a^2+b^2)^2/((a^2+b^2)^2)=1`
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