How to find the complex roots of $x^2-2ax+a^2+b^2$? 
How to find the complex roots of $x^2-2ax+a^2+b^2$?

I tried using the quadratic formula:
$$ x_{1,2} = \frac{2a \pm \sqrt {4a^2-4b^2}}{2} = {a \pm \sqrt {a^2-b^2}} = a\pm \sqrt{a-b}\sqrt{a+b}$$
I tried to represent each root as $x+iy$ but got stuck along the way.
What should I do? 
Thanks

$x^2 - 2ax + a^2 + b^2 = 0 \Rightarrow (x - a)^2 = -b^2 \Rightarrow x = a \pm ib.$
