If ` (p+iq)/(r+is) = x + iy ` , prove that `(p-iq)/(r-is) = x -iy and (p^(2)+q^(2))/(r^(2)+s^(2))=x^(2)+y^(2)` ,where `p,q,r,s,x,y,inR`

Explanation

wer have `(p+iq)/(r+is)=x+iy`
` Rightarrow ((bar(p+iq))/(r+is)) = bar(x + iy ) `
`Rightarrow ( p-iq)/( r+is) =x -iy `
Now, ` (p+iq)/( r+is) =x +iy and (p-iq)/(r-is) = x -iy `
`Rightarrow ((p+iq)/(r+is)) xx ((p-iq)/(r-is)) = (x+iy) (x-iy)`
` Rightarrow ((p+iq)(p -iq))/((r +is)(r-is)) = (x+iy)(x-iy)`
` Rightarrow (p^(2)+q^(2))/(r^(2)+s^(2))=x^(2)+y^(2)` ( Hence proved)