Find the real and imaginary parts of the complex number `(a+ib)/(a-ib)`

Explanation

`(a+ib)/(a-ib)= ((a+ib)^(2))/((a+ib)(a-ib))`
`=(a^(2)-b^(2)+2aib)/(a^(2)+b^(2))`
`=((a^(2)-b^(2))/(a^(2)+b^(2)))+i((2ab)/(a^(2)+b^(2)))`
`:.` Real part `=(a^(2)-b^(2))/(a^(2)+b^(2))`
Imginary part `=(2ab)/( a^(2)+ b^(2))`