# Having trouble with complex quadratic equations

## Main Question or Discussion Point

All,

I am not sure how to handle this situation with complex numbers. Can you help?

Q = A^2 + ABi

Where Q is a complex number.

Can we not solve for A if we know Q and Bi using a quadratic equation?

0 = A^2 + ABi + -Q

Let...

Q = 455
Bi = -22

And in this case I do know that A = 35. However...

When,

a = 1
b = -22
c = -455

Solving...

A = ( -1 +/- Sqrt { 1 - ( 4 * -22 * -455 )}) / 2

I do not get A = 35. Any idea why and what I may be doing wrong?

Thanks,

Jeff

Hurkyl
Staff Emeritus
Gold Member
You messed up while substituting values into the quadratic formula.

Show...

Hurky,

Could you show me what you mean? Where did I mess up?

J

You have confused what the problem is. You are using A in place of X, then you turn around and act like it is something else.

Hurkyl
Staff Emeritus
Gold Member
Hurky,

Could you show me what you mean? Where did I mess up?

J
There are 5 places in the quadratic formula where you need to substitute a number. You got three of them wrong. You know the quadratic formula, right? The solutions to

ax² + bx + c = 0

are

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

right? Just double check your work!

You have confused what the problem is. You are using A in place of X, then you turn around and act like it is something else.
I'm quite sure he did not make that mistake.

Oops...

Hurky,

Okay, I was placing a in place of b in the quadratic equation. Stupid mistake. Thanks greatly. Now I get the correct answer.

Jeff