Solve an equation with complex numbers

  • #1

Homework Statement


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

Homework Equations





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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
51
0
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
22,129
3,298
I can't really see an equation anywhere. All I see is an expression in [itex]\omega[/itex]. An equation must contain an "=".
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Yes, that's a quadratic. What it isn't is an equation! What is the problem really? Do you know the quadratic formula?
 
  • #5
51
0
Sorry, I thought he meant to factor it. Good point!
 
  • #6
1,800
53
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:

[tex]w^2-6.2iw-20=0[/tex]

(I heard a quack)

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

[tex]w^2-aw-20=0[/tex]

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

[tex]w=\frac{6.2i\pm\sqrt{(6.2i)^2+80}}{2}[/tex]

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

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