Đặt `z=a+bi` `(a;b\in RR)`
`=>{z+i}/{z-i}={a+bi+i}/{a+bi-i}`
`={a+(b+1)i}/{a+(b-1)i}`
`={[a+(b+1)i].[a-(b-1)i]}/{[a+(b-1)i].[a-(b-1)i]}`
`={[a^2-(ab-a)i+(ab+a)i-(b^2-1).(-1)]}/{a^2+(b-1)^2}`
`={a^2+b^2-1+2ai}/{a^2+(b-1)^2}`
`={a^2+b^2-1}/{a^2+(b-1)^2}+{2a}/{a^2+(b-1)^2}i`