Answer
$x = a - bi$ is a solution to the equation $x^2 -2ax + (a^2 + b^2) = 0$ (As proved in the step by step work)
Work Step by Step
To solve $x^2 -2ax + (a^2 + b^2) = 0$,
by quadratic formula,
$x = \frac{-(-2a) \pm \sqrt{(-2a)^2 - 4(a^2+b^2)}}{2}$
$x = \frac{2a \pm \sqrt{4a^2 - 4a^2 - 4b^2}}{2}$
$x = a \pm \sqrt{-1}\cdot b$
$x = a \pm bi$
Therefore, $x = a - bi$ is a solution to the equation $x^2 -2ax + (a^2 + b^2) = 0$.
