# Having trouble with complex quadratic equations

1. Jan 2, 2007

### Jeff Cook

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

2. Jan 2, 2007

### Hurkyl

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

3. Jan 2, 2007

### Jeff Cook

Show...

Hurky,

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

J

4. Jan 2, 2007

### robert Ihnot

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.

5. Jan 3, 2007

### Hurkyl

Staff Emeritus
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!

I'm quite sure he did not make that mistake.

6. Jan 3, 2007

### Jeff Cook

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