what is the quadratic equaiton for a quadratic polynomial with complex constants?
Thanks
You mean an equation of the form $\displaystyle Aix^2+Bix+Ci =0$ ?
It's the exact same as quadratic equation with real coefficients.
$\displaystyle \frac{-b \pm \sqrt{b^2-4ac}}{2a}$.
Where:
$\displaystyle a = Ai $
$\displaystyle b = Bi $
$\displaystyle c = Ci $
You can show this by completing the square, which is how we derive the formula for real coefficients.