# quadratic equation for complex numbers

• Jan 15th 2009, 07:53 PM
CarmineCortez
what is the quadratic equaiton for a quadratic polynomial with complex constants?

Thanks
• Jan 15th 2009, 08:31 PM
Mush
Quote:

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.
• Jan 15th 2009, 09:00 PM
mr fantastic
Quote:

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.