I'm trying to solve the problem given below by using a formula given in my reference book
The question is...
Find real values of x and y for which following equation is satisfied:
$$\frac{x-1}{3+i}+\frac{y-1}{3-1}=i$$
where $i=\sqrt{-1}$.
When i use the division formula for complex numbers i.e.:
$$\frac{(x_1x_2+y_1y_2)+i(x_2y_1-x_1y_2)}{x_2^2+y_2^2}$$
Where $x_1$ and $x_2$ are real parts of given complex numbers and $y_1$ and $y_2$ are imaginary parts of given complex numbers.
So when I use the above formula to simplify and reduce the given equation to standard form i.e.:
$$X + iY$$
I get the wrong answer, while when I don't use the formula and manually solve the question stepwise I get right answer.
My question is that why this formula is not working in this case while it works in all other cases???
Thanks in advance