# Solve an equation with complex numbers

1. Dec 7, 2011

### 2slowtogofast

1. The problem statement, all variables and given/known data
I am doing a problem where I have to design a controller for a system. I have to solve the below equation for ω

3.1 (ω)^2 - 6.2iω - 20

2. Relevant equations

3. The attempt at a solution

I am not sure how to start It looks like a quadratic but I don't know what to do with the i
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 7, 2011

### Mike706

Looks like a quadratic, quacks like a quadratic. It is probably quadratic. You can use all the normal methods to solve it. The i is just part of the coefficient of the linear term.

3. Dec 7, 2011

### micromass

I can't really see an equation anywhere. All I see is an expression in $\omega$. An equation must contain an "=".

4. Dec 7, 2011

### HallsofIvy

Yes, that's a quadratic. What it isn't is an equation! What is the problem really? Do you know the quadratic formula?

5. Dec 7, 2011

### Mike706

Sorry, I thought he meant to factor it. Good point!

6. Dec 7, 2011

### jackmell

Ok, it's the "i" that's causing the problem for him. That's intimidating to a lot of students not familiar with complex variables.

The think to do 2slow is not be intimidated by them. Treat them just like constants but remember the complex arithmetic i times i is minus one. So you have:

$$w^2-6.2iw-20=0$$

(I heard a quack)

alright, that 6.2i is just a constant. Treat it just like if you were solving:

$$w^2-aw-20=0$$

as long as you remember to do the complex arithmetic with i's so:

$$w=\frac{6.2i\pm\sqrt{(6.2i)^2+80}}{2}$$

Not gonna' have problems with that (6.2i)^2 thing right?