# Math Help - quadratic equation for complex numbers

1. ## quadratic equation for complex numbers

what is the quadratic equaiton for a quadratic polynomial with complex constants?

Thanks

2. Originally Posted by CarmineCortez
what is the quadratic equaiton for a quadratic polynomial with complex constants?

Thanks
You mean an equation of the form $Aix^2+Bix+Ci =0$ ?

It's the exact same as quadratic equation with real coefficients.

$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$.

Where:
$a = Ai$

$b = Bi$

$c = Ci$

You can show this by completing the square, which is how we derive the formula for real coefficients.

3. Originally Posted by CarmineCortez
what is the quadratic equaiton for a quadratic polynomial with complex constants?

Thanks
The same as it is when the coefficients are real. It doesn't matter that one or more of a, b and c are not real.