## Solve an equation with complex numbers

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

 PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire
 Recognitions: Gold Member 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.
 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus I can't really see an equation anywhere. All I see is an expression in $\omega$. An equation must contain an "=".

Recognitions:
Gold Member
 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?